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CatalogⅠ What is a Ballast Resistor ?Ⅱ Types of Ballast Resistors2.1 Fixed Resistors2.2 Self-Variable ResistorsⅢ The Working Principle of  Ballast ResistorsⅣ Ballast Resistor – Uses and Applications4.1 Ballast Resistor in Fluorescent Lamps4.2 Ballast Resistor for Automotive Applications4.3 Ballast Resistor in a LED CircuitⅤ Symptons of Failture Ballast-ResistorⅥ Frequently Asked Questions about Ballast resistors Introduction  “Ballast” is generally considered as “something that provides stability in English dictionary.  ” Thus, when we refer to an electrical ballast, we are referring to an electrical device that is important in maintaining the stability of the electrical circuit. However, you might be wondering how it provides stability. Depending on the circuit in which they are used, some electric ballasts limit current while others limit voltage. By doing so, they reduce the risk of overvoltage or overcurrent in the circuit, thereby improving system stability. The complexity of electric ballast varies greatly. It can be as simple as a resistor, capacitor, inductor, or a combination of these, or as complex as the electronic ballast found in fluorescent lamps.  Ⅰ What is a Ballast Resistor ? A ballast resistor is an electronic component that is usually used to regulate the current in a circuit. Some devices, such as fluorescent lamps, can exhibit negative resistance characteristics, and an increase in current will result in a decrease in voltage. Negative resistance can cause damage to the power supply or equipment. Ballast resistors are usually connected in series with the negative load, taking advantage of the fact that all components in the series circuit receive the same current. Some ballasts are just series resistors, while others use capacitors and more complex components. Figure1: complex components Ⅱ Types of Ballast ResistorsA resistor is a current-limiting electronic component that can reduce circuit voltage and current. Ballast resistors are classified into three types: fixed, variable, and reactive.2.1 Fixed ResistorsThis genre of ballast resistors have a fixed resistance. A high resistance value is primarily taken considered for most applications. This genre of ballast resistor is commonly used in simple circuits with low-powered loads such as neon or LED lamps. This fixed resistor is also applied to control the ventilation fan speed. It employs a fixed ballast resistor with two center taps. The fan speed selector switch detours portions of the ballast. Therefore, the entire ballast resistor is suitable for full speed, while no section of the ballast resistor is suitable for the low speed.2.2 Self-Variable ResistorsThese ballast resistors have the property of resistance in response to changes in current, such as an increase in current increasing resistance and a decrease in current decreasing resistance. Incandescent lamps frequently use these ballast resistors. As the current through the lamp increases, the ballast resistor heats up, and the resistance rises with the temperature, as does the voltage drop across the resistor. When the current is down, the temperature of the ballast resistor decreases as well, as does its resistance and thus the voltage drop. The benefits of using this type of ballast resistor are that it provides more precise current control than a suitable fixed resistor. Another benefit is that the power lost in the resistive ballast is decreased because a smaller section of the overall power is lost in the ballast when compared to a fixed resistor. Ⅲ The Working Principle of  Ballast Resistors When 220V 50HZ AC power is applied to the switch closed circuit, the current flows through the ballast, and the lamp filament starter heats the filament（The starter was turned off in the beginning. The gas arc discharge in the jumping bubble in the starter caused the bimetallic sheet to heat and deform due to the application of an AC voltage greater than 190V, and the two electrodes were close together to form the filament heated by the passage.) Because there is no arc discharge when the two electrodes of the starter are close together, the bimetal cools and the two poles separate. As the ballast is inductive, when the circuit is suddenly interrupted, 600V is generated at both ends of the lamp for about 1ms. The pulse voltage is -1500V; the exact voltage value depends on the type of lamp. When the lamp discharges, the voltage at both ends drops immediately. At this point, the ballast limits the lamp current on the one hand while also supplying power on the other. There is a phase difference of 55° to 65° between the voltage and the working current of the lamp in order to keep the secondary starting voltage of the lamp stable.Figure2:  the working principle of  a ballast resistor Due to its simple structure, inductive ballast, as the first type of ballast to work with fluorescent lamps, has a relatively large market share. However, on account of its low power factor, poor low-voltage startup performance, heavy energy consumption, stroboscopic and many other shortcomings , its market is gradually being replaced by electronic ballasts. The energy consumption of inductive ballasts: 40W (lamp tube power) + 10W (inductive ballast self-heating consumption) is equal to the total power 50W consumption of the whole set of lamps and lanterns. An electronic ballast is a converter that converts low frequency alternating current power to high frequency alternating current power. Its basic operation is as follows: after passing through a radio frequency interference (RFI) filter, full-wave rectification, and a passive (or active) power factor corrector (PPFC or APFC), the industrial frequency power supply becomes a DC power supply. The output of high-frequency AC power of 20K-100KHZ is added to the LC series resonant circuit connected to the lamp via the DC/AC converter to heat the filament, but the lamp is "discharged" into the "on" state and then enters the light-emitting state. At this point, the high-frequency inductor limits the current increase, ensuring that the lamp tube receives the voltage and current required for normal operation. Various protection circuits, such as abnormal protection, surge voltage, and current protection, temperature protection, and so on, are frequently constructed to improve reliability. Ⅳ Ballast Resistor – Uses and Applications Ballast resistors are most commonly used to adjust the current to a negative resistance load. They can also be applied in other contexts. Fixed ballast resistors are common in low-power devices like light-emitting diodes (LEDs) and neon lights. LEDs are a positive resistive load that can benefit from ballast resistors. 4.1 Ballast Resistor in Fluorescent Lamps Fluorescent lighting, as we all know, is a popular and efficient lighting system. However, there is a disadvantage to using this type of lighting system. When directly connected to a voltage source, it heats up very quickly. This situation is due to the lamp's uncontrollable current draw as soon as its operation. A ballast resistor, connected in series with the lamp, is applied to the circuit to prevent overheating caused by excessive current draw. Therefore, the function of ballast resistor is to regulates the current and reduces the voltage. However,  for the lamp to light up, an arc has to be formed between its two electrodes. This necessitates a high starting voltage that is nearly equal to the supply voltage. The ballast resistor provides the required voltage during startup, and then immediately after an arc is established, it reduces the voltage while also regulating the current flow. Figure3: application in fluorescent lamp 4.2 Ballast Resistor for Automotive Applications Ballast resistors are generally included in the ignition kits of automotive machines such as automobile engines. Such devices are often called Ignition Ballast Resistors because of their application. The application of this device reduces the possibility of coil failure. It is connected between the ignition coil's primary voltage source and the coil stud. This connection helps to reduce the coil voltage and coil current, so the coil does not get as hot as it would without it, extending the coil's life. However, a high voltage equal to the primary voltage source is required to start the ignition engine. As a result, a jumper wire is frequently connected to the ballast resistor. This jumper wire provides the voltage required to start the engine.  Figure4: application in automotives 4.3 Ballast Resistor in a LED Circuit If the source voltage in an LED circuit is greater than the rated voltage of an LED lamp, the LED may be damaged. It is strongly advised to connect a ballast resistor in series with the lamp to avoid this case. By connecting the ballast resistor in this manner, the voltage across the LED is down to a tolerable level. The circuit diagram for the same is shown in the figure below.  Figure5: application in leds  The following formula is the value of resistance of the ballast :R = (E – Vf)/IFWhere: R= resistance of the ballast resistorE = voltage sourceVf = forward voltage of the LEDIF =Forward current of the LED. So, let's say you have an LED with a voltage rating of 4 volts, a forward current of 10 mA, and a voltage source of 6 volts. This means that the voltage across the LED should be 4 or less than 4 volts. As a result, the resistance of the ballast resistor should be R= (6-4)/0.010 = 200 or greater. Now that we've covered the applications briefly, let's look at the different types of ballast resistors on the market. Ⅴ Symptons of Failture Ballast-Resistor A ballast resistor is a device in your car that limits the amount of current flowing through an electric circuit. Because they did not have the benefit of circuit boards like most modern vehicles, ballast resistors are commonly found in older vehicles. Normal wear and tear can damage the ballast resistor over time, so there are a few things to look for if you suspect a bad or failing ballast resistor needs servicing. 1. Vehicle starts, then immediately goes out The most obvious symptom is that the vehicle starts but then dies as soon as you remove the key. If this occurs, Your Mechanic's experts will be able to measure the voltage coming from the ballast resistor and determine if it needs to be replaced. They will inform you of the condition of your ballast resistor once they have read the voltage. 2. Not starting at all The vehicle will not start if the ballast resistor is not functioning properly. Because it is an electrical system, it is best left to the professionals. The only way to get the vehicle running again is to replace the ballast resistor. 3.  Don’t jump the resistor Some people attempt to jump the resistor, which means that the ballast resistor is ignored and the extra current is routed to the points. The points are not designed to withstand the additional voltage, causing them to wear out and fail prematurely. This will result in a much more extensive repair than if the ballast resistor was replaced at the start. Furthermore, because you are tampering with electricity, it can be dangerous, especially if you don't know what you're doing. 4.  Let the vehicle beIf your ballast resistor is out of work, your vehicle will not start and you will need to have it towed to a mechanic's shop. Because the professionals at Your Mechanic make house calls, you will be able to save money on towing. Furthermore, because the vehicle will not start, it is not a dangerous situation as long as you leave it alone. Do not attempt to bypass the ballast resistor and do not continue to try to start the engine. Allow the professionals to repair it so you can get back on your way. Ⅵ Frequently Asked Questions about Ballast resistors 1. Is a ballast resistor necessary?　If the coil required a ballast resistor when it was used with points, then you must still use the resistor. If it didn't, then no resistor is necessary. The ballast resistor keeps the engine running by preventing the engine from receiving full amperage from the ignition once started.　 2. Why do ignition coils need ballast resistor?　In simple terms, the ballast resistor in a Mopar limits the amperage, or current flow, through the coil while the engine is running, thereby extending the life of the coil and breaker points of the distributor. 3. How do you know if a ballast resistor is bad?To test your ballast resistor you need an ohm meter or multimeter set to ohms. Remove the connectors from both sides of the resistor. The ohms should read between 1.8 and 5 ohms. You should be getting 9 volts to the positive side of the coil. 4. What causes a ballast resistor to fail?The resistance through the ballast resistor varies with current flow which varies with engine rpm. This naturally causes the resistor to expand and contract from heat. That's why they eventually fail. 5. Can a resistor wire go bad?　　The only way the wire will "go bad" is if it gets a break in it so it has infinite resistance (an open circuit). 6. Which circuit the ballast resistor is used?　　Ballasts can also be used simply to limit the current in an ordinary, positive-resistance circuit. Prior to the advent of solid-state ignition, automobile ignition systems commonly included a ballast resistor to regulate the voltage applied to the ignition system. 7. What is inside of a ballast?　A magnetic ballast (also called a choke) contains a coil of copper wire. The magnetic field produced by the wire traps most of the current so only the right amount gets through to the fluorescent light. That amount can fluctuate depending on the thickness and length of the copper wire. 8. What's the difference between a ballast and non ballast coil? Basically, a non-ballast coil is designed to produce full spark output with 12 volts on the input (+ terminal). A ballast coil is designed to produce the same spark output, but with only 6 to 9 volts on the input. 

"What Are Input and Output Impedance in Op-Amps?" - "1.1 Impedance Overview" -> "Understanding Impedance Basics" - "1.2 Input Impedance of Op-Amp" -> "Why Does an Op-Amp Need High Input Impedance?" - "1.3 Output Impedance of Op-Amp" -> "Why Does an Op-Amp Need Low Output Impedance?" - "1.4 Ideal Op Amp Impedance" -> "Ideal vs. Practical Op-Amp Impedance" - "Ⅱ High Input Impedance and Low Output Impedance Effect" -> "The Effects of High Input and Low Output Impedance" - "Ⅲ How to Calculate Input Impedance and Output Impedance" -> "How to Calculate Op-Amp Impedance"- Missing or improvable schema types detected: Missing Article schema, FAQPage schema.- Sections with vague/unsupported claims: "A small amount of current is decreased by any electrical input..." (Rewritten for technical accuracy: "Every electrical input sources or sinks a small amount of leakage current."); Formula for impedance was inverted (ΔI/ΔV instead of ΔV/ΔI) and has been corrected.- Estimated content freshness score: 5/10-->Summary: Operational amplifiers (op-amps) rely on extremely high input impedance to prevent signal degradation and very low output impedance to drive loads effectively. Understanding how to calculate and optimize these impedance values is critical for preventing loading effects and ensuring accurate signal amplification in modern circuit design.IntroductionThe input and output impedance of an amplifier is the ratio of voltage to current flowing in or out of these terminals. The input impedance may depend upon the source supply feeding the amplifier, while the output impedance may also vary according to the load impedance (RL) across the output terminals. Ideally, op-amps are supposed to have zero output impedance and infinite input impedance. However, practical op amp input impedance and output impedance are finite, making them critical factors in the design of any robust electronic circuit. What Are Input and Output Impedance in Op-Amps?Understanding Impedance BasicsIn electronic circuits, impedance defines the complex relationship between voltage and current. It is a combination of resistance (which is frequency-independent) and reactance (which is frequency-dependent, driven by inductors and capacitors). The input impedance of an op-amp acts as the load impedance to the preceding signal source. Conversely, the output impedance of the op-amp acts as the source impedance to the subsequent load receiving the amplified signal. Understanding these parameters is essential for proper impedance matching and signal integrity.Why Does an Op-Amp Need High Input Impedance?While the input impedance of an ideal op-amp is assumed to be infinite, practical devices always draw a microscopic amount of bias current. Every electrical input sources or sinks a small amount of leakage current, which can be modeled as a high-value resistor connected in parallel to the input terminals. Modern CMOS op-amps can achieve input impedances in the tera-ohm ($10^{12} Omega$) range, drastically reducing this current draw.Although input impedance is typically represented as a simple resistor, the input terminals also possess a tiny parasitic capacitance. At lower frequencies, this capacitance is negligible. However, at high frequencies, this parasitic capacitance provides a substantial load for AC signals, hindering rise and fall times and potentially causing severe signal distortion.Why Does an Op-Amp Need Low Output Impedance?An ideal amplifier should be capable of driving infinite current into any load without voltage loss, but practical op-amps have strict physical limitations. For instance, the widely used LM358 op-amp can typically source only 40mA and sink 20mA of current. This restriction in the output drive capability is modeled as a small internal resistor placed in series with an ideal voltage source.Because the actual output voltage is measured after this internal resistor, overloading the op-amp causes a significant voltage drop across it. Consequently, the delivered voltage falls short of the amplifier's intended output. To counter this limitation when driving heavy loads, engineers often add an external discrete output stage (like a push-pull transistor buffer) to boost current capacity.Ideal vs. Practical Op-Amp ImpedanceAn ideal op-amp features infinite input impedance and zero output impedance. Infinite input impedance ensures that absolutely no current flows into or out of the inverting and non-inverting terminals. Zero output impedance guarantees that the output voltage remains perfectly stable, regardless of the current demanded by the load.ParameterIdeal Op-AmpPractical Op-Amp (e.g., CMOS)Input ImpedanceInfinite (∞)Very High (Mega-ohms to Tera-ohms)Output ImpedanceZero (0 Ω)Very Low (10 to 100 ohms)Op Amp Impedance MatchingThe Effects of High Input and Low Output ImpedanceHigh input impedance ensures that the amplifier draws virtually no current from the preceding signal source. Because op-amps are primarily voltage-gain devices, their core task is to convert a low-energy, voltage-driven signal into a higher-voltage output without distorting the original source.Preventing the Loading Effect: If the input impedance were low, the op-amp would draw excessive current, causing a voltage drop across the source's internal resistance and degrading the signal.Maximizing Voltage Transfer: According to Ohm's Law (V=IR), a higher input impedance ensures that the maximum possible voltage drops across the amplifier's input terminals rather than being lost in the source wiring.Safe Current Management: Low impedance circuits can inadvertently trigger high current draws, which may damage sensitive sensor outputs. High input impedance safely isolates these delicate components. How to Calculate Op-Amp ImpedanceImpedance is mathematically represented by the ratio of voltage variation (ΔV) to current variation (ΔI). For an op-amp, the variation in the input common-mode voltage range is measured against the variation in the input bias current to determine dynamic input impedance.Input Impedance and Output Impedance of AmplifierUsing the voltage divider principle, you can determine the actual input and output voltages of an amplifier based on its gain, source impedance, and output impedance. The formula for the effective input voltage is:Vin = Vsource • (Zin / (Rs + Zin)) ......(1)Where Vin is the actual voltage the amplifier receives, Vsource is the original source voltage, Zin is the amplifier's input impedance, and Rs is the source's internal impedance.Similarly, you can calculate the voltage delivered to the load:Vload = Vout • (Rload / (Rload + Zout)) ......(2)Where Vload is the voltage dropped across the load, Vout is the amplifier's internal generated output voltage, Rload is the load resistance, and Zout is the amplifier's output impedance.To measure the output impedance practically, you can model it as a Thevenin equivalent circuit:Zout = Vo / Isc ......(3)Where Vo is the open-circuit output voltage, and Isc is the short-circuit output current. This formula assumes a strictly linear relationship between the output voltage and current.ConclusionOp-amps are essential in circuit designs where the input impedance must be vastly larger than the source impedance, and the effective output impedance must be infinitesimal compared to the load. The specific demands of your application will dictate the required precision of the op-amp. Ultimately, the input and output impedance of amplifiers stem from internal parasitic resistance and capacitance. By understanding these physical limits and applying the correct voltage divider formulas, engineers can design highly efficient, distortion-free amplification stages. Frequently Asked QuestionsWhat happens if an op-amp has low input impedance?If an op-amp has low input impedance, it draws excessive current from the signal source. This creates a loading effect, causing a significant voltage drop across the source's internal resistance. Consequently, the amplifier receives a degraded signal, leading to inaccurate amplification and potential signal distortion.Which type of op-amp provides the highest input impedance?Modern CMOS (Complementary Metal-Oxide-Semiconductor) and JFET operational amplifiers provide the highest input impedance. Unlike older bipolar junction transistor models like the LM741, CMOS op-amps can achieve input impedances in the tera-ohm range, drawing nearly zero bias current from the source.How does a unity-gain buffer utilize impedance matching?A unity-gain buffer leverages the op-amp's extremely high input impedance and near-zero output impedance to bridge circuits. It prevents a low-impedance load from drawing too much current from a high-impedance source, ensuring the signal voltage transfers perfectly without degradation or power loss.Can you measure op-amp output impedance directly with a multimeter?No, you cannot measure an active op-amp's output impedance directly using a standard multimeter's resistance setting. Instead, you must calculate it dynamically by measuring the open-circuit output voltage, applying a known load resistor, measuring the loaded voltage drop, and using the voltage divider formula.{ "@context": "https://schema.org", "@graph":[ { "@type": "Article", "headline": "Op Amp Input and Output Impedance Guide", "datePublished": "2021-01-23T15:45:51Z", "dateModified": "2026-03-19T15:12:00+08:00", "author": { "@type": "Organization", "name": "ApogeeWeb" }, "publisher": { "@type": "Organization", "name": "ApogeeWeb" } }, { "@type": "FAQPage", "mainEntity":[ { "@type": "Question", "name": "What happens if an op-amp has low input impedance?", "acceptedAnswer": { "@type": "Answer", "text": "If an op-amp has low input impedance, it draws excessive current from the signal source. This creates a loading effect, causing a significant voltage drop across the source's internal resistance. Consequently, the amplifier receives a degraded signal, leading to inaccurate amplification and potential signal distortion." } }, { "@type": "Question", "name": "Which type of op-amp provides the highest input impedance?", "acceptedAnswer": { "@type": "Answer", "text": "Modern CMOS (Complementary Metal-Oxide-Semiconductor) and JFET operational amplifiers provide the highest input impedance. Unlike older bipolar junction transistor models like the LM741, CMOS op-amps can achieve input impedances in the tera-ohm range, drawing nearly zero bias current from the source." } }, { "@type": "Question", "name": "How does a unity-gain buffer utilize impedance matching?", "acceptedAnswer": { "@type": "Answer", "text": "A unity-gain buffer leverages the op-amp's extremely high input impedance and near-zero output impedance to bridge circuits. 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Introduction: A Comprehensive Guide to Using a Multimeter in 2025When it comes to measuring instruments, the question often arises: how do you use a multimeter effectively? A Multimeter, also known as a VOM (volt-ohm-milliammeter) or DMM (Digital Multimeter), is the indispensable "Swiss Army Knife" for electronics. It is used to measure two or more electrical values—principally voltage (volts), current (amps), and resistance (ohms) in electronic and electrical circuits.In 2025, modern multimeters have evolved significantly. Beyond basic measurements, many now include features like capacitance testing, transistor checks, temperature sensing, and even Bluetooth connectivity for smartphone data logging. Whether you are troubleshooting a smart home device, checking automotive wiring, or testing a battery, the multimeter is your primary diagnostic tool.Multimeters are generally divided into two types: analog multimeters and digital multimeters (DMM). While analog meters use a moving needle, digital versions are now the industry standard, offering high accuracy, auto-ranging capabilities, and easy-to-read LCD or OLED displays. This guide is designed for beginners and will cover the basic parts, working principles, functions, and safety tips for using a multimeter in the modern era.Ⅰ What are the Parts of a Multimeter?The anatomy of a multitester generally includes a display (scale or screen), a selection knob, ports (jacks), and test probes. However, the interface differs between the older analog style and modern digital tools.Analog Multimeters: Use a microammeter with a moving pointer (needle) to display readings against a printed scale. They require the user to interpret the scale based on the selected range.Digital Multimeters (DMM): The current mainstream choice. They feature a numeric digital display, often with a backlight for dark environments. Modern DMMs may also include "True RMS" for accurate AC readings and auto-ranging features that automatically select the correct measurement scale for you.A common digital multimeter is composed of three main interface parts:1.1 The Display (Meter Head)On a digital multimeter, this is the LCD or LED screen where measurement values are shown. It often displays icons for battery life, high voltage warnings, and the unit of measurement (e.g., V, A, Ω). High-end models in 2025 may feature high-resolution color screens or bar graphs that mimic analog needles to show fluctuating signals.1.2 Measuring Circuit (Internal)Hidden inside the case, the measuring circuit converts incoming analog signals (voltage, current, resistance) into digital data. It is composed of precision resistors, an Analog-to-Digital (A/D) converter, and protective fuses to ensure safety during overload.1.3 Rotary SwitchThe central dial allows you to select the function (Volts, Amps, Ohms) and the range. In Auto-ranging multimeters, you simply select the function (e.g., DC Voltage), and the meter automatically adjusts to the scale of the signal. In Manual-ranging meters, you must select the specific range (e.g., 20V, 200V) yourself.Ⅱ Working Principle of MultimeterA Digital Multimeter (DMM) works by converting an analog input signal into a digital value using an A/D converter. The core logic involves comparing the input voltage against a reference voltage.To measure current and resistance, the multimeter actually uses voltage as the base reference:Current: The meter measures the voltage drop across a known internal shunt resistor.Resistance: The meter outputs a small, known current through the component being tested and measures the resulting voltage to calculate resistance (Ohm's Law).Modern DMMs use complex logic control circuits to manage the display, auto-ranging, and safety checks, ensuring that the reading on the screen is stable and accurate. Ⅲ Multimeter Operating ProceduresTo ensure accuracy and safety—especially with modern high-energy circuits—follow these steps:Safety Check: Inspect your test leads for damaged insulation. Ensure the multimeter is rated for the voltage you are testing (e.g., CAT III or CAT IV ratings for household mains).Select Function: Turn the rotary dial to the correct setting (Voltage, Current, or Resistance) before connecting the probes.Select Range: If using a manual-ranging meter and the value is unknown, always start at the maximum range and switch down to lower ranges to get a precise reading. Auto-ranging meters handle this automatically.Zero Calibration: For resistance measurements on analog meters, touch the probes together and zero the needle. Digital meters usually auto-zero, but you can check the "Rel" (Relative) mode on advanced models to null out lead resistance.Power Off for Resistance: Never measure resistance or continuity on a live circuit. Turn off the power to the device before testing.Probe Handling: Keep your fingers behind the finger guards on the test probes to avoid electric shock.Ⅳ Common Multimeter FunctionsMeasure Resistance (Ohms - Ω)Ensure the circuit power is OFF. Connect the test leads across the component (resistor, coil, etc.). Note: Measuring a component while it is soldered to a PCB may give inaccurate results due to parallel paths from other components.Measure Current (Amps - A/mA)Critical Step: You must physically move the red probe to the specific "Amps" or "mA" jack on the multimeter. The meter must be connected in series with the circuit (you must break the circuit and let current flow through the meter). Warning: Connecting a meter in current mode across a voltage source (parallel) will blow the meter's fuse.Measure Voltage (Volts - V)Connect the meter in parallel (across the component or power source). Ensure you select AC (V~) for wall outlets or DC (V=) for batteries.Detect Short Circuit (Continuity)Set the dial to the continuity mode (often marked with a sound wave symbol). Touch probes to two points. If resistance is near zero (a short), the multimeter will beep. This is excellent for checking broken wires or fuses.Non-Contact Voltage (NCV)Many modern multimeters (2020s era and later) include an NCV sensor at the tip. This allows you to detect the presence of live AC voltage in a wire or outlet without touching the metal contacts.Test ICs and ComponentsWhile multimeters can check supply voltage (VCC) and ground pins on Integrated Circuits (ICs), troubleshooting internal IC logic is often better done with an oscilloscope or logic analyzer. However, a multimeter is perfect for finding shorted pins. Ⅴ Multimeter Usage Tips1. Probe Safety: Never touch the metal tips of the probes during a test. Always hold the insulated handles behind the finger guards.2. Switching Gears: Never rotate the selection dial while the probes are connected to a live high-voltage circuit. This can cause internal arcing. Disconnect probes, switch modes, then reconnect.3. Battery Maintenance: If the multimeter will not be used for a long period, remove the internal battery to prevent leakage and corrosion.4. High Voltage Awareness: Be aware of the "CAT" rating of your meter. Do not use a CAT II meter for main service panels (which require CAT III or CAT IV ratings).Video: How to Use a Multimeter?Ⅵ How to Find Circuit Faults with Multimeter6.1 General Troubleshooting Strategy1. Visual InspectionBefore measuring, look for charred components, swollen capacitors, or loose wires. Touching components (cautiously) to check for overheating can also identify shorts.2. Voltage TracingMeasure the voltage at various points in the circuit starting from the power source. If voltage is present at point A but missing at point B, the fault lies between them (e.g., a broken trace or failed component).3. Hidden TroubleshootingIntermittent failures are often caused by "cold" solder joints or loose connectors. Continuity mode is vital here. Wiggle wires while testing continuity; if the beep stops, you have found a loose connection. 6.2 Measuring Techniques6.2.1 Voltage Measuring PointsTesting voltage against a "Ground" reference is the standard method. Connect the black probe to the circuit Ground (GND) and use the red probe to touch various test points (VCC, output pins). Deviations from the expected voltage (e.g., getting 2V on a 5V line) usually indicate a problem.6.2.2 Measuring Parameters Selection① Always check if you are measuring AC or DC. Measuring AC voltage while in DC mode (or vice versa) will give false readings.② For signal circuits, remember that standard multimeters measure "Average" or "RMS" voltage. They may not accurately show fast data pulses—an oscilloscope is required for that.③ Polarity: In DC mode, if you reverse the probes (Red on negative, Black on positive), the screen will simply show a negative sign (e.g., -12V). This is normal and safe for digital meters. Ⅶ How to Measure Current with Digital MultimeterMeasuring DC Current1. Insert the Red test lead into the jack marked "mA" (for low current) or "10A/20A" (for high current). Insert the Black lead into "COM".2. Turn the dial to the DC Current setting (A=).3. Break the circuit: You must physically interrupt the wire and place the multimeter probes in line with the circuit so current flows through the meter.4. Power on the circuit and read the value.Figure 1. Measuring Operating Current of a DC Relay If the reading is negative, your probes are reversed (current is entering the black probe). This does not damage a digital meter.Figure 2. Measuring DC Current in Series Measuring Current with an Analog MultimeterWith analog meters, polarity matters. If you connect probes backward, the needle will deflect to the left (below zero), potentially damaging the mechanism. Always ensure Red connects to the more positive side and Black to the negative side.Figure 3. Series connection with Analog Multimeter Figure 4. Reading the Scale on an Analog Multimeter Measuring AC CurrentThe process is similar to DC, but you must select the AC Current setting (A~). For high currents (e.g., household mains), it is highly recommended to use a Clamp Meter instead of a standard multimeter for safety. A clamp meter measures current via magnetic fields without breaking the circuit.Figure 5. AC Measurement Diagram Ⅷ Which is Better: Analog or Digital Multimeter?For 99% of users in 2025, the Digital Multimeter (DMM) is superior. It offers higher accuracy, higher input impedance (which means it doesn't affect the circuit you are testing), and easier readability. Analog meters are now a niche tool, primarily used by technicians who need to see real-time trends or rapid fluctuations that a digital digital might miss (though modern DMMs with "bar graphs" solve this).Analog MultimeterDigital MultimeterVisualizes trends/fluctuations easily via needle movement.Easy to read exact numbers; no parallax errors.Lower input impedance (can load down sensitive circuits).High input impedance (better for delicate electronics).Susceptible to damage from physical shock (drops).generally more rugged and durable.Often requires manual zeroing and range selection.Includes Auto-ranging, Auto-polarity, and specialized functions.Both meters have their place, but if you can only afford one, buy a Digital Multimeter. They are now available at very affordable price points without sacrificing essential accuracy. Ⅸ Best Multimeter Brands in 2025When selecting a multimeter, reliability and safety are paramount. Brands differ by their target audience: Professionals (industrial use) vs. Hobbyists (home use). Below are reputable brands recognized in the industry today.*Etekcity (Budget/Home)Mastech GroupInnova (Automotive)Klein ToolsKeysight Technologies (formerly Agilent)BrymenKaiweets / AstroAI (Budget)Fluke (Professional Gold Standard)ExtechAmprobeHioki Ⅹ Frequently Asked Questions1. What is a multimeter primarily used for?A digital multimeter is a diagnostic tool used to measure electrical values—principally voltage (Volts), current (Amps), and resistance (Ohms). It is standard equipment for electricians, automotive mechanics, and HVAC technicians. 2. What is "Auto-Ranging"?Auto-ranging is a feature on digital multimeters where the meter automatically selects the correct measurement range for the signal it detects. You simply select "Voltage," and the meter decides if it's millivolts or hundreds of volts. This saves time and prevents setup errors. 3. Why is "True RMS" important?True RMS (Root Mean Square) allows a multimeter to accurately measure AC voltage even when the sine wave is distorted (common in motor drives, HVAC systems, and computers). Non-True RMS meters are only accurate on perfect sine waves. 4. Can I use a multimeter to test a battery?Yes. Set the multimeter to DC Voltage (V=). Connect the red probe to the positive (+) terminal and black to negative (-). A fully charged 1.5V AA battery should read greater than 1.5V (usually 1.6V). If it reads below 1.2V, it is dead. 5. What are CAT ratings?CAT ratings (Category I, II, III, IV) define the safety level of the meter. CAT III or CAT IV is recommended for testing household wiring and mains power to protect against dangerous transient voltage spikes.

IntroductionOperational amplifier (op amp for short) is basically a voltage amplifying device designed to be used with components like capacitors and resistors, between its in/out terminals, or is simply a linear Integrated Circuit (IC) having multiple-terminals. In electronics, the open-loop voltage gain of the actual operational amplifier is very large, which can be seen a differential amplifier with infinite open loop gain, infinite input resistance and zero output resistance. In addition, it has positive and negative inputs which allow circuits that use feedback to achieve a wide range of functions. And meanwhile, it can be further simplified into an ideal op amp model, referred to as an ideal op amp (also called ideal OPAMP).CatalogIntroductionⅠ Ideal Op Amp Characteristics1.1 Infinite Input Resistance1.2 Zero Output Impedance1.3 Infinite Open-loop Gain1.4 Infinite Common-mode Rejection Ratio1.5 Infinite BandwidthⅡ Assumptions of Ideal Op AmpⅢ Working Characteristics of Ideal Operational Amplifiers3.1 Work in Linear Region3.2 Work in Nonlinear RegionⅣ Analysis of Ideal Operational Amplifier CharacteristicsⅤ Balanced Resistance Presets5.1 The Role of Balanced Resistance5.2 Input Balancing Resistor ExplanationⅥ Ideal Op Amp EquationsⅦ Several Common Op Amp CircuitsⅧ Difference Between Ideal Op-amp and Practical Op-ampⅠ Ideal Op Amp CharacteristicsWhen analyzing various application circuits of operational amplifiers, the integrated operational amplifier is often regarded as an ideal operational amplifier. The so-called ideal op amp is to idealize various technical indicators of op amps, and it must have the following characteristics.Characteristics of An Ideal Op-Amp1.1 Infinite Input ResistanceThe input terminal of an ideal operational amplifier does not have any current to flow in. In electronics, op amps are voltage gain devices. They amplify a voltage fed into the op amp and give out the same signal as output with a much larger gain. In order for an op amp to receive the voltage signal as its input, the voltage signal must be dropped across the op amp. If you know the concept of a voltage divider, voltage drops primarily across components with high impedances, proportionally according to ohm’s law by the formula V=IR. So the greater the resistance (or impedance) of a device, the greater the voltage drop across that device is. To make sure that the voltage signal drops fully on the op amp, it must have a very high input impedance, so that the voltage drops fully across it. If it had a low input impedance, the voltage may not drop across it and it would not receive the signal. This is why op amps must have high-input impedances.It’s also easy to make the input impedance lower (put a resistor in parallel) or the source impedance higher (put a resistor in series).Figure 1. Ideal Op Amp Symbol and Transfer Characteristic Curve 1.2 Zero Output ImpedanceThe output of an ideal op amp is a perfect voltage source, no matter how the current flowing to the amplifier load changes, the output voltage of the amplifier is always a certain value, that is, the output impedance is zero. In practice, zero output impedance is actually a distinct property from infinite input impedance, but for a very long time infinite input impedance was approached only with compromises in offset voltage and noise. 1.3 Infinite Open-loop GainIn an open-loop state, the differential signal at the input has an infinite voltage gain. This feature makes the operational amplifier very suitable for practical applications with upper negative feedback configuration. 1.4 Infinite Common-mode Rejection RatioAn ideal operational amplifier can only respond to the difference between the voltages at both ends of V+ and V-. In addition, the same part of the two input signals (ie common mode signal) will be completely ignored. What’s more, a high CMRR is required when a differential signal must be amplified in the presence of a possibly large common-mode input, such as strong electromagnetic interference (EMI). An example is audio transmission over balanced line in sound reinforcement or recording. 1.5 Infinite BandwidthThe ideal operational amplifier will amplify the input signal of any frequency with the same differential gain, which will not change with the change of signal frequency.Ⅱ Assumptions of Ideal Op AmpThe op amp can be considered a voltage controlled current source, or it is an integrated circuit that can amplify weak electric signals. Based on it, for an ideal OPAMP, what is the relationship between it and these electrical signals?First, assume that the current flowing into the input of the op amp is zero. This assumption is almost completely correct for FET op amps, because the input current for FET op amps is below 1pA. But for dual high-speed op amps, this assumption is not always correct, because the input current of it can sometimes reach tens of microamperes.Second, assume that the gain of the op amp is infinite, so the op amp can swing the output voltage to any value to meet the input requirements. It means that the output voltage of the op amp can reach any value. In fact, when the output voltage is close to the power supply voltage, the op amp will saturate. Maybe this hypothesis does exit, but needs a limit in practical. For example, at higher frequencies, the internal junction capacitors of transistor come into play, thus reducing the output and therefore the gain of amplifier. The capacitor reactance decreases with increase in frequency bypassing the majority of output. The opamp is in saturation state.Figure 2. Op Amp SaturationFor example, as per datasheet of LM741, large signal voltage gain is 200V/mv. It means an open loop gain of 200,000. If you operate an op-amp in open-loop condition(i.e. without negative feedback) ,even microvolts of input voltage (input offset voltage of LM741 is 3mv) will drive the output to saturation.In most of the amplifier circuits op-amp is configured to use negative feedback which greatly reduces the voltage gain (i.e. closed loop gain). In oscillators and schmit triggers, Op-amp is configured to use positive feedback. Comparator circuit is an example of the circuit which utilizes open-loop gain of op-amp. Its output will be always at saturation either positive or negative saturation. In an integrator circuit, the DC gain should be limited by adding a feed back resistor in parallel with capacitor ;else the output will get saturated .Even in amplifier circuits, the amplitude of the input signal and the voltage gain of the circuit should be balanced so that the output voltage does not exceed power supply voltage . For example for a non-inverting amplifier with a voltage gain of 100, the maximum permissible input voltage will be 150 mv if the VCC is 15 Volts. If you apply a signal of 200 mv ,the op-amp output will goto saturation as the required output will be 20 volts which exceeds the VCC of 15 Volts.Third, the assumption of infinite gain also means that the input signal must be zero. The gain of the op amp will drive the output voltage until the voltage (error voltage) between the two input terminals is zero. The voltage between the two input terminals is zero. The zero voltage between two input terminals means that if one input terminal is connected to a hard voltage source like ground, the other input terminal will also be at the same potential. In addition, since the current flowing into the input terminal is zero, the input impedance of the op amp is infinite.Fourth, of course, the output resistance of an ideal op amp is zero. An ideal op amp can drive any load without any voltage drop due to its output impedance. At low currents, the output impedance of most op amps is in the range of a few tenths an ohm, so this assumption is true in most cases. Ⅲ Working Characteristics of Ideal Operational Amplifiers3.1 Work in Linear RegionWhen the ideal op amp works in the linear region, the output and the input voltage show a linear relationship. Where u0 is the output voltage of the integrated op amp; u+ and u- are the voltages at the non-inverting input terminal and the inverting input terminal, respectively. Auo is the open loop differential voltage magnification. According to the characteristics of the ideal op amp, two important characteristics of the ideal op amp in the linear region.1) Zero differential input voltageSince the open-loop differential voltage magnification of an ideal op amp is equal to infinity, and the output voltage is a certain value, the voltage values at the non-inverting input terminal and the inverting input terminal are approximately equal. Just like short circuit between input and output, but it is fake. Because it is an equivalent short circuit, not a real short circuit, so this phenomenon is called "virtual short".2) Zero input currentSince the open-loop input resistance of an ideal op amp is infinite, no current flows into the op amp at either input. At this time, the current at the non-inverting input terminal and the inverting input terminal are both equal to zero. Like an disconnection, but an equivalent disconnection, so this phenomenon is called "virtual break". Virtual short and virtual break are two important concepts for analyzing the ideal op amp working in the linear region.In fact, the ideal operational amplifier has the characteristics of "virtual short" and "virtual break". These two characteristics are very useful for analyzing linear amplifier circuits. The necessary condition for virtual short is negative feedback. When negative feedback is introduced, at this time, if the forward terminal voltage is slightly higher than the reverse terminal voltage, the output terminal will output a high voltage equivalent to the power supply voltage after the amplification of the op amp. In fact, the op amp has a respond time changing from the original output state to the high-level state (the golden rule of analyzing analog circuits: the change of the signal is a continuous change process). Due to the feedback resistance of the reverse end change will inevitably affect its voltage, when the reverse end voltage infinitely close to the forward end voltage, the circuit reaches a balanced state. The output voltage does not change anymore, that is, the voltage at the forward end and the reverse end is always close. (Note: The analysis method is the same when the voltage decreases.) 3.2 Work in Nonlinear RegionWhen the op-amp operates in the nonlinear region, the output voltage no longer increases linearly with the input voltage, but saturates. The ideal op amp also has two important characteristics when operating in the nonlinear region.1) When u+ ≠ u-, the output voltage of the ideal op amp reaches the saturation value.When u+ > u-, the op-amp operates works in positive saturation region with a positive output voltage.When u+ < u-, the op-amp operates works in negative saturation region with a negative output voltage.Ideal op amp operates in the nonlinear region, u+ ≠ u-, there is no “virtual short”.2) The input current is equal to zero.Although the input voltage u+ ≠ u- above, the input current is considered to be zero. Ⅳ Analysis of Ideal Operational Amplifier CharacteristicsAs for Op-amp, there's probably a description like this: three-terminal element (circuit structure with double-ended input, single-ended output), ideal transistor, high-gain DC amplifier.(1) High input resistanceUnder this situation, the current flowing into the input terminal is close to 0, almost no signal source current is used, which is close to the voltage control characteristic. And virtual break is derived from this.(2) Lower output resistanceIt has the characteristics of adapting to any load. And the impedance of the subsequent load circuit will not affect the output voltage.(3) Infinite voltage amplification(4) Under a certain supply voltage condition, the amplifier can only work in closed-loop (negative feedback) mode, and the actual amplification is limited. Because op-amps themselves don't have a 0V connection but their design assumes the typical signals will be more towards the center of their positive and negative supplies. Thus, if your input voltage is right at one extreme or forces the output toward one supply, chances are it won't work properly. Working in open-loop mode is the like a comparator, and the output is high level orlow level.In the closed-loop (limited amplification) state, the amplifier is randomly compare the potentials of the two input terminals. The output stage makes immediate adjustments when they are not equal. So the final purpose of amplification is to make the potentials of the two input terminals equal. And virtual short is derived from this. Ⅴ Balanced Resistance Presets5.1 The Role of Balanced Resistance1) A suitable resistance is generally required to ensure that the input impedance is matched.2) In order to reduce the input current imbalance, the in-phase resistor should be equal to the parallel value of the two resistors at the reverse end in theory. In practice, as a result of the closed loop, especially in deep negative feedback conditions, the misalignment is not obvious at the output. And there is no need of in-phase grounding resistor when the misalignment is not the main problem. Because a balanced resistor is the starting point for an ideal op amp. In-phase grounding resistance is useful for bipolar op amps, and has no meanings for MOS-type op amps.3) Ground input termination resistance: it is necessary for impedance matching and high frequency setting.4) Bias current and offset current.For operational amplifiers with bias current greater than offset current, input resistance matching can be reduced, and precision circuits can compensate bias current to a minimum. If the bias current and offset current are similar, the matching resistance will increase the error.5) Set for the bias current at the input, the purpose of which is to equalize the impedance of the invertingand non-inverting inputs, so that two inputs with equal bias currents are assumed to have equal voltage drops, thereby counteraction can be made. 5.2 Input Balancing Resistor ExplanationA op-amp is connected to an inverting amplifier:Set the input resistance for R1, feedback resistance for Rfi,Assume that the non-inverting end is not connected to a balanced resistor, but grounded directly.Set the input bias current for the op-amp IB (same voltage in inverting and non-inverting end).The current flows through R1 and Rf are represented by I1 and If.Inverting voltage is V-, The op-amp gain is A.Use KCL in the inverting end (set the input signal to 0).Where (0-V-)/R1- (A+1)V- /Rf=IBFrom the above equation, it follows that V-=-(IB×R1×Rf/(Rf+(A+1)R1))At this time, the output voltage of the op-amp is Vo=A×(IB×R1×Rf/(Rf+(A+1)R1))The above formula can be approximated as Vo=IB×((A×R1)/Rf)If the in-phase terminal passes through a resistor R2 to ground and R2=R1/Rf, then the voltage at the in-phase terminal is V+=-IB×R2KCL is applied to the inverted terminal, where (0-V-)/R1+(A×(V+-V-)-V-)/Rf=IBAt this time the output voltage of the op-amp is Vo=0. Ⅵ Ideal Op Amp EquationsUnderstanding the basic conditions of an ideal op amp, and combining it with the Kirchhoff's current law (KCL) node voltage method and the superposition theorem of the node, is an effective method to analyze the ideal op amp circuit.As shown below, find the output voltage uoFigure 3. OPAMP Circuit1) Equation based on KCLFrom the concept of virtual break, i+=i-=0, then i1=i2, i3=i4, so (a)Based on virtual break, u+=u-, then (b)2) Node voltage methodList the node voltage equations for node 1 and node 2, and get (c)Note: Because the output current of the op amp is unknown at 1) and 2), it is not possible to list the KCL equation or node voltage equation at the output of the op amp. In addition, the op amp output uo in 2) should be treated as an independent voltage source. 3) Superposition theoremWhen there are multiple signal inputs, choosing the superposition theorem to solve can simplify the analysis and calculation process. The size of the output signal uo can be regarded as the superposition of the output signal obtained by the independent action of u1 and u2. When u1 acts alone, the u2 terminal is grounded, and the op amp output is: (d)Therefore, the final output of the operational amplifier is:   (e) Ⅶ Several Common Op Amp CircuitsNon-inverting Amplifier CircuitA non-inverting amplifier is an op-amp circuit configuration which produces an amplified output signal. It provides a high input impedance along with all the advantages gained from using an operational amplifier. Inverting Amplifier CircuitAn inverting amplifier (also known as an inverting operational amplifier or an inverting op-amp) is a type of operational amplifier circuit which produces an output which is out of phase with respect to its input by 180 degrees out of phase with respect to input signal. In the following figure, two external resistors to create feedback circuit and make a closed loop circuit across the amplifier. Op-amp as AdderAn adder circuit can be made by connecting more inputs to the inverting op amp. The circuit diagram of a summing amplifier is as shown in the following figure. Differential AmplifierDifferential amplifier is an analog circuit with two inputs and and one output in which the output is ideally proportional to the difference between the two voltages. It is a very useful op-amp circuit and by adding more resistors in parallel with the input resistors as shown in the following. Composite AmplifierThe composite amplifier is termed as a combination of multiple operational amplifiers that are cascaded together with a negative-feedback loop around the entire network. The resistance in the circuit is generally selected at the K ohm level, the ratio of the resistance affects the gain and bias, in addition, the supply current, frequency response and capacitive load driving capability of the op amp determine their specific values in circuits. If it is used in a high-frequency circuit, the resistance needs to be reduced to obtain a better high-frequency response, but it will increase the input bias current, thereby increasing the current of the power supply. Ⅷ Difference Between Ideal Op-amp and Practical Op-ampIdeal op amps use no power, have infinite input impedance, unlimited gain-bandwidth and slew rate, no input bias current, and no input offset. They have unlimited voltage compliance.Practical op amps consume some power, have very high input impedance have limited gain-bandwidth and limited slew rate, have some input bias current and input offset voltage. Voltage compliance is limited by the power supply rail, or frequently even less.Still practical op amps are very useful because most of the limitations listed above are way better than what your circuit needs.For an ideal amplifier, it does not draw any current at all from its input. Assuming a two input amplifier the signal current in both input probes is zero. In other words the input impedance must be infinite. The output, should operate as the output of an ideal voltage source. This means that the potential between the output and the ground must be A(v2−v1), no matter how much current would a load connected to the output would draw. In other words the output impedance must be zero.For a real amplifier, the input impedance must be as large as possible while the output impedance must be as low as possible.In fact, An op-amp in real life, however, cannot operate with zero current flow. Frequently Asked Questions about Ideal Op Amp1. What is characteristic of ideal opamp?Ideal op amps will have infinite voltage gain, infinitely high impedance, zero output impedance, its gain is independent of input frequency, it has zero voltage offset, its output can swing positive or negative to the same voltages as the supply rails, and its output swings instantly to the correct value. 2. How does an ideal op amp work?An operational amplifier, or op amp, generally comprises a differential-input stage with high input impedance, an intermediate-gain stage, and a push-pull output stage with a low output impedance (no greater than 100 Ω). ... Open-loop voltage gain runs very high, on the order of 1 million. 3. Why are op amps not ideal?Op-amps with FET inputs have an Ibias that is so small that this method becomes less practical. Instead of measuring the voltage drop across a resistor, one can monitor the change in voltage across a capacitor as it is charged by the bias current. 4. How are real op amps different from ideal op amps?In real op amps, the amplified signal will not fully reach the DC supply rails. They will fall short of it. In an ideal op amp, the output will swing instantly to the amplified voltage value. There will be no time delay between the time the voltage is input into the op amp till the time it is output. 5. What are the four main ideal characteristics of an open-loop op amp?An ideal op amp is usually considered to have the following characteristics:Infinite open-loop gain G = vout / vInfinite input impedance Rin, and so zero input currentZero input offset voltageInfinite output voltage rangeInfinite bandwidth with zero phase shift and infinite slew rateZero output impedance R

IntroductionSemiconductor diode, also known as crystal diode, has obvious unidirectional conductivity. It is a kind of electronic components widely used in electrical equipment for protection, rectification, switching, and many other applications. So it is pretty common to see diodes in daily electronic circuits, such as Zener diodes, light-emitting diodes, photodiodes, etc. Therefore, it is necessary to know how to test whether a diode is properly working or not.How to Test a Diode Using a MultimeterCatalogIntroductionⅠ Diode Basics1.1 To Figure Out Diode Anode and Cathode1.2 What Would Cause a Diode to Fail?1.3 Common Diode Failures AnalysisⅡ How to Test Diode with a Multimeter?2.1 Digital Multimeter and Analog Multimeter2.2 Common Diodes Testing Rules2.3 Testing Methods of Types of DiodesⅢ Example Analysis3.1 Test a Diode in Circuit3.2 Power-off and Power-on Testing Methods3.3 ConclusionⅠ Diode Basics1.1 To Figure Out Diode Anode and CathodeThe anode and cathode of diode can be distinguished by screen printing on PCB board, which are as shown in the following:1) The notched end is the cathode of diode.2) The end with a horizontal bar is the cathode.3) The end with white parallel bars is the cathode.4) One end of the triangle arrow is the cathode.5) The small end of the plug-in diode is the cathode, and another big end is the anode.1.2 What Would Cause a Diode to Fail?The common reasons for a diode failure are open circuit, short circuit and unstable voltage regulation. Among these three types of failures, there may be signs. For example, the power supply voltage rises, the supply voltage drops to zero or the output is unstable. Therefore, specific problems must be analyzed in detail for the diode test.The common measurement tool for diode is a multimeter, including on-circuit measurement (the diode is on the circuit board) and off-circuit measurement (the diode is not on the circuit board). As for the basic principle of diode measurement, the forward resistance and the reverse resistance of the PN junction are measured, and the basic judgment is based on the values of them. Therefore, to do a good job in diode test, it is necessary to understand the basic structure and working principle of diodes, and then to understand the main fault characteristics of the diode. 1.3 Common Diode Failures Analysis1) open circuitThis means that the positive and negative electrodes of the diode have been disconnected, and the forward and reverse resistance of the diode have become infinite. After the diode is open, the circuit is in an open state.2) voltage breakdownThis means that there is a path between the positive and negative electrodes of the diode, and the forward and reverse resistance are as large as or close to each other(but not infinite). After a diode breaks down, the action between the positive and negative electrodes may always exit, because there are different manifestations in different circuits.3) forward voltageIf the forward resistance of the diode is too large, the voltage drop of the signal on the diode will increase, which will cause the output signal to decrease, and the diode will be damaged due to the heat. After the forward resistance becomes larger, the unidirectional conductivity of the diode will become poor.4) reverse voltageThe reverse resistance of the diode becomes smaller, which means the unidirectional conductivity of the diode be effected.5) performance degradationUnder this circumstance, the diode does not have obvious failures such as open circuit or breakdown. However, when the situation is getting worse, the stability of the circuit will deteriorate or the output signal voltage of the circuit will drop. Ⅱ How to Test Diode with a Multimeter?2.1 Digital Multimeter and Analog MultimeterWhen using a digital multimeter to test a diode, the red probe connects with the anode and the black probe connects with the cathode. At this time, the measured resistance is the forward conduction resistance of the diode, which is just the opposite of the test result of an analog multimeter. 2.2 Common Diodes Testing Rules(1) The forward resistance of the low-power germanium diode is 300Ω～500Ω, and the silicon diode is lkΩ or more. The former reverse resistance is tens of thousand ohms, and the latter is above 500kΩ (the value of high-power diode is smaller).(2) The polarity of the diode can be judged according to the resistance values (small forward resistance and large reverse resistance). Set the multimeter to the ohm block (Usually use R×100 or R×1k block, do not use R×1 block or R×10k block. The R×1 block is in a large current, it is easy to burn the tube, while using R×10k block may cause the tube broken down with high voltage). Connect the two polarities of the diode with the test probes respectively, and measure the two resistance values. When the measured resistance value is smaller, the end connected to the black lead is the anode. In the same way, when the measured resistance value is larger, the end connected to the black probe is the cathode. If the measured reverse resistance is small, it means that the diode is short-circuited, on the contrary, if the forward resistance is large, it means that the tube is open. In both cases, the diode can’t be work normally.(3) Silicon diodes generally have a forward voltage drop of 0.6V～0.7V, and the forward voltage drop of a germanium diode is 0.IV～0.3V. By measuring the forward voltage of the diode, it can be judged that the tested diode is a silicon tube or a germanium tube. This method is to connect a resistor (lkΩ) behind the power supply, and then connect with the diode according to the polarity characteristic to make the diode forward conducting. At this time, use a multimeter to measure the tube voltage drop. In addition, it is more convenient if it is used in energized dynamic measurement. 2.3 Testing Methods of Types of DiodesZener DiodesHow to test a Zener diode? The following here is to give some ideas.(1) Generally use the low-resistance block to test the Zener diode with a multimeter. Since the battery in the meter is 1.5V, this voltage is not enough to make the Zener diode reverse breakdown. So the forward and reverse resistance should be the same as a normal diode.(2) Measurement of the voltage stabilization value Vz of the Zener diode. When measuring diode, the power supply voltage must be greater than the stable voltage of the tube under test. In this way, the high-resistance block of the multimeter (R×10k) must be used. At this time, the battery in the meter has a higher voltage. When the multimeter's range is set to high barrier, measure diode reverse resistance. If the measured resistance is Rx, the voltage regulation value of the Zener diode is:In the formula, n is the override of the gear used. For example, if the highest electrical barrier ofR0 is the central resistance of the multimeter.E0 is the highest battery voltage value of the multimeter used.Example: Use an MF50 multimeter to measure a 2CW14 diode.R0=10Ω, the highest electrical barrier is R×10k.E0=15V, the measured reverse resistance is 75kΩ, then its voltage regulation value is:If the measured resistance is very large (close to infinite), it means that the voltage Vz under test is greater than E0, therefore, tube will not break down. If the measured resistance is very small (0 or only a few ohms), it means that the test probes are connected reversely, and then just swap the test probes. Light-emitting Diodes (LED)A light-emitting diode is a semiconductor device that converts electrical energy into light energy. It has the characteristics of small size, low working voltage and low working current.(1) There is a PN junction inside the light-emitting diode, so LED has the same characteristic of unidirectional conductivity. Its detection is similar to the measurement of ordinary diodes.(2) Use the R×1k or R×10k gear, and the forward and reverse resistance values are measured. Generally, the forward resistance is less than 50kΩ, and the reverse resistance is greater than 200kΩ.(3) The working current of the light-emitting diode is an important parameter. If the working current is too small, the light-emitting diode will not light up, and it is too large, the light-emitting diode will be easily damaged.(4) The forward turn-on voltage of the light-emitting diode is 1.2V ~ 2.5V, and the reverse breakdown voltage is about 5V. PhotodiodesPhotodiode is a semiconductor device that can convert light intensity into electrical signals.(1) There is a window on the top of the photodiode that can inject light, and the light irradiates the die through it. Under the excitation of the light, a large number of photoelectric particles are generated in the photodiode, which greatly enhances its conductivity and reduces internal resistance.(2) The photodiode is similar to the Zener diode. It also works in the reverse state, with reverse voltage.(3) The forward resistance of the photodiode does not change with the light. Its reverse resistance is larger when there is no light, and becomes smaller when it is exposed to light. That is, the stronger the light, the smaller the reverse resistance. Without light, the reverse resistance will return to the original value.(4) According to the related principle, use a multimeter to measure the reverse resistance of the photodiode. Change the light intensity when measuring, and observe the change of the reverse resistance of the photodiode. If there is no change or less change of the reverse resistance when light changes, it indicates that the tube has failed. High-speed Switching DiodesThe method of detecting high-speed silicon switching diodes is the same as that of ordinary diodes. The difference is that the forward resistance of this tube is relatively large. Measuring with Rxlk block, the forward resistance value is 5k ~ 10k in general, and the reverse resistance value is infinite. Fast Recovery Diodes / Ultrafast Recovery DiodesDetecting fast recovery and ultra-fast recovery diodes with a multimeter is basically the same as that of detecting plastic-encapsulated silicon rectifier diodes. That is, first use the Rxlk block to test its unidirectional conductivity. Generally, the size of forward resistance is about 4 ~ 5k, and the reverse resistance is infinite. And then use the Rxl block to repeat the test, at this time, the forward resistance is several ohms, and the reverse resistance is still infinite. DIAC (Diode for Alternating Current) DiodesUse the Rxlk block, and measure the forward and reverse resistance values of diac, which should be infinite. If the test probes are exchanged to measure, the pointer swings to the right, which indicates that the test tube has a leakage fault. Another method is placing the multimeter in the DC voltage block. During the test, shake the megohmmeter, and the voltage value indicated by the multimeter is the VBO value of the tube. Then change the two pins of the tested tube, and measure the VBR value in the same way. Finally, compare VBO and VBR. The smaller the difference between the absolute values of the two, the better the symmetry of the diac diode. TVS DiodesFor the dual TVS, resistance values between the two pins should be infinite when the red and black test probes of multimeter are exchanged at random. Otherwise, the tube has poor performance or has been damaged. High-frequency Varistor Diodesa. Identify Diode PolarityThe difference between high-frequency varistor diodes and ordinary diodes is that their color code is different. It is generally black of ordinary diodes, while high-frequency varistor diodes’ is light. Its polarity rule is similar to that of ordinary diodes. That is, the end with the green ring is the cathode, otherwise it is the anode.b. Measure Forward and Reverse ResistanceThe specific method is the same as the method of measuring ordinary diodes. Using the Rxlk block of a AM-500 multimeter, the forward resistance is 5k～55k, and the reverse resistance is infinite. Varactor DiodesUsing Rx10k block, no matter how the red and black test leads are exchanged for measurement, the resistance between the two pins of the varactor diode should be infinite. During the measurement, if the multimeter swings slightly to the right or the resistance value is zero, it means that the varactor diode under test has a leakage fault or has been broken down. No matter the loss of varactor diode capacity or internal open-circuit fault, it is impossible to detect them with a multimeter. When necessary, the replacement method can be used for inspection to make judgment. Infrared Light Emitting Diodes (IRED)Put the multimeter in the Rxlk block and measure the forward and reverse resistance of the IRED diode. Generally, the forward resistance should be about 30k, and the reverse resistance should be above 500k. It means the tube can work normally. The larger the reverse resistance, the better. IR Receiver Diodesa. Appearance Identification: Diode Cathode / Anode(1) Common infrared receiving diodes are black in appearance. In addition, there is a small oblique plane at the top of the tube body of the infrared receiving diode. Usually, the pin with one end of the oblique plane is the negative pole and the other end is the positive pole.(2) Use the Rxlk block to test the resistances between two pins. When a diode works normally, the resistance value of two pins are different. And exchange the test leads several times to get some pairs of values. According to the smaller resistance value, the pin connected to the red probe is the cathode, and the pin connected to the black probe is the anode.b. Performance DetectionUse a multimeter to measure the forward and reverse resistance of the infrared receiving diode. According to the resistance values, whether the diode is damaged can be judged preliminarily. Laser DiodesUse the Rxlk block of multimeter, and determine the order of the pins of the laser diode according to the method of detecting ordinary diodes. Because the forward voltage drop of the laser diode is larger than that of the ordinary diode, when detecting the forward resistance, the pointer of the multimeter is slightly deflected to the right, and the reverse resistance is infinite. Unijunction Transistor (UJT)a. Discrimination of ElectrodesBased on the R×1k block, use two meter pens to measure the forward and reverse resistance between any two of the three electrodes ( base B1 and base B2, and emitter E) of the ujt diode. The measured resistance values between the two electrodes are both 2~10kΩ, in addition, B1 and B2 will be different.b. Performance JudgmentThe performance of an ujt diode can be judged by measuring whether the resistance between its pins is normal. Use the R×1k barrier, the black test lead connect to the emitter E, and the red test lead connect to the two base electrodes in turn. Normally, a resistance value should be several thousand to ten thousand ohms. On the contrary, the red test lead connects to the emitter E, and the black test lead connects to the two base electrodes in turn, and the resistance should be infinite under normal conditions. The forward and reverse resistance values between the two bases are both in the range of 2~10kΩ. If they differ greatly from the normal value, the diode is damaged. Ⅲ Example Analysis3.1 Test a Diode in Circuita. Diode Test UsingAnalog MultimeterThe following measurements are all based on silicon diodes. If it is a germanium diode, the forward and reverse resistance of the diode will decrease.1) Measure forward resistance FRThe following figure is a wiring schematic diagram for measuring the forward resistance of a diode with an analog multimeter:Give the result as follows:IndicatorDescriptionUse the R×1k block to measure the diode, the forward resistance is several thousand ohms, and the pointer indicates stability. If the pointer swings slightly, it indicates that the thermal stability of the diode is poor.If the pointer indicates hundreds of kiloohms when measuring the forward resistance, it means that the diode is open.If the pointer indicates tens of kiloohms, it indicates that the diode has a large forward resistance and poor diode performance. Description of measurement of forward resistance:Forward Resistance (FR)DescriptionThousands of ohmsNormalZero or much less than a few thousand ohmsBreakdownHundreds of kilosLarge FR, the diode is openDozens of kilohmsLarge FR, bad forward characteristicsThe pointer is unstablePoor stability 2) Measure reverse resistance RRThe following figure is a wiring schematic diagram for measuring the reverse resistance of a diode with an analog multimeter:Give the result as follows:IndicatorDescriptionWhen measuring the reverse resistance, the value should be several hundred kiloohms. The larger the resistance value is, the better the indicator should be stable.If the reverse resistance is only a few thousand ohms, it means that the diode has broken down and has lost its unidirectional conductivity. Description of measurement of reverse resistanceReverse ResistanceDescriptionHundreds of kilosNormalZeroBreakdownMuch less than a few hundred thousand ohmsDiode’s reverse characteristic is not good.Pointer does not moveThe diode is open. Note: The reverse resistance of some diodes is very large, at this time, it is not certain that the diode is open, so that its forward resistance should be measured. If the value is normal, it means that the diode is not open.Pointer is unstableThe pointer cannot be stabilized at a certain resistance value during measurement, indicating that the diode has poor stability. 3.2 Power-off and Power-on Testing MethodsDiode in-circuit measurement is divided into two situations: Power-off and Power-on statea. Power-off MeasurementThere are something should be noted the method of this test.The influence of the external circuit on the test result is the same as the resistance and capacitance measured of internal circuit. And the influence of the measured forward resistance by the external circuit is lower than the reverse resistance.If there is any doubt about the measuring result, the diode should be removed from the circuit and measured separately. b. Power- on MeasurementWhen the circuit board is powered on, the test point is the tube voltage drop. Because the diode has a very important characteristic: when it is turned on, the tube voltage drop is basically unchanged. So the voltage drop is normal after being turned on, that is to say, the diode is normal.Measurement method: The diagram below shows the connection diagram of the tube voltage drop after the diode in the DC circuit. Setting multimeter in DC voltage 1 V block, the red probe is connected to the cathode of the diode, and the voltage indicated is the forward voltage drop of the diode. Diode forward voltage drop measurement results are analyzed as follows:DiodeDescriptionSilicon diode0.6VThe diode is normal and in a forward conducting state.> 0.6VThe diode is not in the conducting state.Close to 0The diode is in a breakdown state, the current in the loop will increase.Germanium diode0.2VThe diode is normal and in a forward conducting state.> 0.2VThe diode is off or is faulty.Close to 0In the breakdown state, the loop current increases significantly, without unidirectional conductivity. 3.3 ConclusionThe following points should be noted when measuring diodes:1) The diode in AC is in the cut-off state, because the diode is in the reverse state, and the reverse voltage at both ends is very large. The average voltage across the diode measured by the DC block is negative at this time.2) Use different blocks of the same multimeter to measure positive and negative resistance of one diode, their values will different. The forward and reverse resistances of the same diode measured with different multimeters are also different.3) When measuring the forward resistance of a diode, if the pointer cannot stop at a certain resistance value and constantly swings, it indicates that the thermal stability of the diode is not good.4) Some multimeters will provide a “diode check” function that displays the actual forward voltage of the diode when its conducting current. Such meters typically indicate a slightly lower forward voltage than what is “nominal state” for a diode, due to the very small amount of current used during the measurement. Frequently Asked Questions about Diode Test1. What is a diode test?A diode is best tested by measuring the voltage drop across the diode when it is forward-biased. ... A multimeter's Diode Test mode produces a small voltage between test leads. The multimeter then displays the voltage drop when the test leads are connected across a diode when forward-biased. 2. How do you test a rectifier diode?Touch the red (positive) probe of the multimeter to the positive terminal of the diode closet to the welder case interior. Touch the black (negative) probe of the multimeter to the negative terminal of the same diode. The multimeter should read a resistance between 0 and 1 ohm, or the diode is faulty. 3. How can you tell if a diode is positive or negative?Sometimes it's easiest to just use a multimeter to test for polarity. Turn the multimeter to the diode setting (usually indicated by a diode symbol), and touch each probe to one of the LED terminals. If the LED lights up, the positive probe is touching the anode, and the negative probe is touching the cathode. 4. How do you test a Schottky diode?Connect the red positive test lead to the anode of the Schottky diode and the black common test lead to the cathode of the diode. Listen for a “beep” or a “buzz” from the multimeter. If the Schottky diode responds as expected, the multimeter will sound a tone. 5. Can I test a diode in circuit?A diode is best tested by measuring the voltage drop across the diode when it is forward-biased. A forward-biased diode acts as a closed switch, permitting current to flow. A multimeter's Diode Test mode produces a small voltage between test leads. ... Voltage may be present in the circuit due to charged capacitors. 6. How do you check a diode?Diode PolarityThe polarity of both diodes is indicated with a stripe on one end of the body. The stripe corresponds to the line in the schematic symbol, indicating the cathode. The other end (no stripe) is the anode, indicated by the triangle in the schematic symbol. 7. What happens when a diode fails?However, a failed diode can short out too. In this case, the diode will exhibit a small resistance in both directions. The common reasons for a diode failure are excessive forward current and a large reverse voltage. Usually, large reverse voltage leads to a shorted diode while overcurrent makes it fail open. 8. How can you tell if a diode is blown?Turn the dial to “diode test” mode.This level of current is high enough to produce a reading, yet not so high that the diode will fail. It may also be labeled as “diode check” on your multimeter and is usually indicated by a small diode symbol. The diode symbol will look like a triangle pointing towards a line.

IntroductionResistors are usually connected in a circuit in various ways, and the two most basic ways are series and parallel. This article will mainly introduce these two connection methods, including their definitions, formulas, circuit diagrams, examples and identification methods. In addition, the article also introduces Ohm's law and Kirchhoff's law, which are very important in understanding the series and parallel connections of resistors.You may need these two calculators in reading this arrticle:① Ohm's Law Calculator② Parallel and Series Resistance CalculatorThe following video explains the basics of resistors in series and parallel, which can promote your understanding of this article. But it does not matter so much if you skip this video since the article explains in detail and is comprehensive.Resistors in series and parallel - deriving the formulaCatalogIntroductionCatalogI Series Connection of ResistorsII Parallel Connection of ResistorsIII Resistor Combination(Mixed Resistor Circuit)IV Ohm's Law  4.1 What is Ohm's Law?  4.2 What is Closed Circuit Ohm's Law?  4.3 The Key Points of Studying Ohm's LawV Kirchhoff's Law  5.1 Concepts  5.2 Kirchhoff's First Law (Nodal Current Law)  5.3 Kirchhoff's Second Law (Law of Loop Voltage)  5.4 Application Note of Kirchhoff's LawVI Series and Parallel Circuit Identification MethodsVII QuizⅧ FAQI Series Connection of Resistors(1) Circuit characteristicsFigure1. Resistors in seriesThe figure shows the series connection of n resistors, and the voltage and current reference directions are related. The circuit characteristics are derived from Kirchhoff’s law:(A) The resistors are connected in sequence. According to KCL, the current flowing through the resistors is the same;(B) According to KVL, the total voltage of the circuit is equal to the sum of the voltages of the series resistors, namely:(2) Equivalent resistanceFigure2. Equivalent resistance circuitSubstituting Ohm's law into the voltage expression, we get:The above formula illustrates that the series circuit of multiple resistors in Figure (a) and the circuit of single resistor in Figure (b) have the same VCR, which is equivalent to each other.The equivalent resistance is:In conclusion:The resistors are connected in series, and the equivalent resistance is equal to the sum of the sub-resistances;The equivalent resistance is greater than any one of the series resistance.The partial pressure of series resistanceIf the total voltage across the series resistor is known, what is the divided voltage on each resistor? From figure (a) and figure (b) we know:MeetIn conclusion:Resistors are connected in series, and the voltage on each sub-resistor is proportional to the resistance value. The higher the resistance value, the higher the voltage. Therefore, the series circuit can be used as a voltage divider circuit.Example 1: Calculate the voltage across the two series resistors as shown in the figure.Figure3. Circuit of Example1Solution: From the partial pressure formula of series resistance:(Note the direction of U2)(3) PowerThe power of each resistor is:SoTotal power:Draw conclusions from the above formulas:When resistors are connected in series, the power consumed by each resistor is proportional to the size of the resistor, that is, the larger the resistance, the larger the power consumed;The power consumed by the equivalent resistance is equal to the sum of the power consumed by each series resistor.II Parallel Connection of Resistors(1) Circuit characteristicsFigure4. Parallel circuit characteristics The figure shows the parallel connection of n resistors, and the voltage and current reference directions are related. The circuit characteristics are derived from Kirchhoff's law:(a) The two ends of each resistor are connected together. According to KVL, the two ends of each resistor are at the same voltage;(b) According to KCL, the total current of the circuit is equal to the sum of the currents flowing through the parallel resistors, namely:(2) Equivalent resistanceFigure5. Equivalent resistance in parallel connectionSubstituting Ohm's law into the current expression, we get:G =1/R is the conductanceThe above formula illustrates that the parallel circuit of multiple resistors in Figure (a) and the circuit of single resistor in Figure (b) have the same VCR, which is equivalent to each other.The equivalent conductance is:Therefore,Namely,The most commonly used formula to find the equivalent resistance when two resistors are connected in parallel:In conclusion:The resistors are connected in parallel, and the equivalent conductance is equal to the sum of the conductances and greater than the partial conductance;The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the sub-resistances, and the equivalent resistance is less than any parallel sub-resistance.Current distribution of parallel resistanceIf the total current of the parallel resistance circuit is known, find the current on each sub-resistance and call it a shunt. From figure (a) and figure (b) we know:Namely,MeetFor two resistors in parallel, there are:Conclusion: When the resistors are connected in parallel, the current on each sub-resistor is inversely proportional to the resistance value, and the current divided by the larger resistance value is smaller. Therefore, the parallel resistor circuit can be used as a shunt circuit.(3) PowerThe power of each resistor is:SoTotal power:Draw conclusions from the above formulas:When resistors are connected in parallel, the power consumed by each resistor is inversely proportional to the size of the resistor, that is, the larger the resistance, the smaller the power consumed;The power consumed by the equivalent resistor is equal to the sum of the power consumed by each parallel connected resistor.consumed by each series resistor.III Resistor Combination(Mixed Resistor Circuit)A circuit with resistors connected in series and connected in parallel is called a resistor combination or mixed resistor circuit. The part where the resistors are connected in series has the characteristics of a resistor series circuit, and the part where the resistors are connected in parallel has the characteristics of a resistor parallel circuit.Example 2: The circuit is shown in the figure, please calculate the voltage and current of each branch.Figure6. Example circuit 2Solution: This is a resistor series and parallel circuit. First find the equivalent resistance Reg = 11W, and the current and voltage of each branch are:The general steps for solving series and parallel circuits can be obtained from the above examples:⚫ Find the equivalent resistance or equivalent conductance;⚫ Apply Ohm's law to find the total voltage or total current;⚫ Apply Ohm's law or voltage division and shunt formula to find the current and voltage on each resistor.Therefore, the key issue in analyzing series-parallel circuits is to distinguish the relationship between series and parallel circuits.To determine the series-parallel relationship of the circuit, the following 4 points should be mastered:⚫ Look at the structural characteristics of the circuit. If two resistors are connected end-to-end, they are connected in series;⚫ Look at the relationship between voltage and current. If the current flowing through the two resistors is the same current, it is connected in series; if the two electrical groups bear the same voltage, it is connected in parallel.⚫ Equivalent to deformation of the circuit. For example, the left branch can be twisted to the right, the upper branch can be turned down, the curved branch can be straightened, etc.; the short circuit in the circuit can be compressed and extended at will; the multi-point grounding can be connected by a short circuit . Generally, if it is really a problem with a resistor series circuit, it can be distinguished.⚫ Find the equipotential point. For circuits with symmetrical characteristics, if two points can be judged to be equipotential points, according to the concept of circuit equivalence, one is to use short wires to connect the equipotential points; the other is to break the branch that connects the equipotential points. Open (because there is no current in the branch), thus obtain the series-parallel relationship of the resistance.IV Ohm's Law4.1 What is Ohm's Law?(1) The content of Ohm's lawWhen there is a potential difference between the two ends of the conductor, an electric field appears inside the conductor, and the charge moves in a directional motion under the force of the electric field to generate current. German physicist Ohm summed up Ohm's law in 1826 through a large number of experiments: Under steady conditions, the intensity of the current passing through a section of conductor is proportional to the voltage across the conductor.(2) Mathematical expression of Ohm's law Note: The unit of the physical quantity in the formula: the unit of I is ampere (A), the unit of U is volt (V), and the unit of R is ohm (Ω).The proportional coefficient R in the formula is determined by the properties of the conductor and is called the resistance of the conductor. Unit: Ohm (Ω). The reciprocal of resistance is called conductance and is represented by G, that isUnit: Siemens (S).(3) Understanding and explanation of Ohm's law● Applicable conditions of Ohm's law: applicable to pure resistance circuits (that is, when working with electrical appliances, the consumed electrical energy is completely converted into internal energy.)● I, U and R in the formula must correspond to the same conductor or the same circuit. If it is in different time, different conductor or different section of circuit, I, U, and R can not be mixed, therefore, the three physical quantities should be marked with angles in order to distinguish under normal circumstances.● For the same conductor (that is, R does not change), I and U are proportional; for the same power source (that is, U does not change), I and R are inversely proportional.● R=ρL/S is the definition of resistance, which means that the resistance of a conductor is determined by the material, length and cross-sectional area of ​​the conductor itself. In addition, resistance is also related to factors such as temperature.● The formula transformed from Ohm's law is a measure of resistance. It indicates that the resistance of a conductor can be given by U/I, that is, the ratio of R to U and I is related, but the magnitude of R itself is related to the applied voltage U and the passing current Factors such as the size of I are irrelevant.● Knowing any two quantities among I, U and R, you can find another quantity.● Issues that need special attention and re-emphasis: I, U and R in the formula must be in the same circuit; when using the formula to calculate, the unit of each physical quantity must be unified.The above explanations are all part of Ohm’s law, which only applies to pure resistance circuits.(4) Pure resistance circuitA pure resistance circuit is a circuit with only resistance elements in addition to the power supply, or inductance and capacitance elements, but their influence on the circuit is negligible. The voltage and current have the same frequency and phase.The resistance converts all the energy obtained from the power supply into internal energy. This kind of circuit is called a pure resistance circuit. Here is a brief explanation from the energy point of view.Basically, as long as there is no conversion of electric energy other than internal energy, this circuit is a pure resistance circuit.4.2 What is Closed Circuit Ohm's Law?In an AC circuit, Ohm's law also holds, but the resistance R should be changed to impedance Z, that is, I = U/Z. If the circuit is closed and contains a power supply, it is called a full circuit, as shown in the figure below. The dotted line in the figure is the power supply, which is called an internal circuit. The circuit outside the power supply is called an external circuit. Since the power supply has internal resistance, the current not only has a voltage drop when passing through an external circuit, but also has an internal voltage drop when passing through an internal circuit. In the whole circuit, the current intensity is proportional to the electromotive force E of the power supply, and inversely proportional to the resistance (R+r) of the whole circuit (including the inner circuit and the outer circuit). This is the Ohm's law of the whole circuit, expressed by the formula:Where I- the current in the circuit, A; E- the electromotive force of the power supply, V; R- the resistance of the external circuit, Ω; r- the resistance of the internal circuit, Ω.From the above formula, in the circuit shown in the figure below, E=IR+Ir=Uouter+Uinner.Figure7. The simplest closed circuitIn the formula, U external = IR-external circuit voltage; U internal = Ir-internal circuit voltage.It should be noted that, since the internal resistance of the power supply itself and the internal resistance of the connecting wires are generally not large, the calculation results that are ignored in the calculation are basically correct. But sometimes it is necessary to calculate the internal voltage drop of the power supply, and to accurately calculate the current of the whole circuit, it is necessary to use the whole circuit Ohm's law. For example, in the figure below, if E=10V, r=0.1Ω, R=1kΩ, then:Figure8. An application example of Ohm's law of closed circuit① When S is connected to the 1 position, the circuit is in the open state,Ammeter readingThe reading of the voltmeter is U=IR=0.01×1000=10 (V), or U=E-Ir=10-0.01×0.1≈10 (V).②When S is connected to the 2 position, the circuit is in an open state, so the reading of the ammeter is 0; the reading of the voltmeter is U=E=10(V).③When S is connected to the 3 position, the circuit is in a short-circuit state, the reading of the ammeter is I=E/r=10/0.1=100(A)A; the reading of the voltmeter U=0(V).4.3 The Key Points of Studying Ohm's LawOhm's law is an important basic law in electricity. It is a law that is summarized and summarized through experiments. To master this law, we must pay attention to the following points:(1) Ohm's law applies to the entire circuit or a part of the circuit from the positive pole to the negative pole of the power supply, and it is a pure resistance circuit.(2) The current I "passing through" in Ohm's law, the voltage U at "both ends" and the resistance R of the "conductor" are all corresponding physical quantities on the same conductor or the same circuit. The above relationship does not exist between the current, voltage, and resistance of different conductors. Therefore, when using the formula I=U/R, the current, voltage, and resistance of the same conductor or the same circuit must be substituted into the calculation, and the three correspond one to one.(3) There is simultaneity among the three physical quantities in Ohm’s law. Even on the same part of the circuit, the closing or opening of the switch and the movement of the sliding position of the sliding varistor will cause the change of the circuit, which will lead to the current in the circuit. , Voltage, resistance changes, so the three quantities in the formula I=U/R are the same time value.(4) The difference between I=U/R and R=U/I:Ohm's law expression I=U/R means that the current in the conductor is related to the voltage across the conductor and the resistance in the conductor. When the resistance R is constant, the current I in the conductor is proportional to the voltage U across the conductor; when the voltage U across the conductor is constant, the current I in the conductor is inversely proportional to the resistance R of the conductor.R=U/I is derived from Ohm’s law expression. It means that the resistance value of a certain section of conductor is equal to the ratio of the voltage across the section of the conductor to the current passing through it. This ratio R is the property of the conductor itself and cannot be understood as R is directly proportional to U and inversely proportional to I. This is also the difference between physics and mathematics.(5) Ohm's law reflects the causal relationship between current intensity and voltage, and the restrictive relationship between current intensity and resistance under certain conditions. That is, when the resistance is constant, the current intensity is proportional to the voltage across the conductor; when the voltage is constant, the current intensity is inversely proportional to the resistance of the conductor. When establishing a proportional relationship, we must pay attention to its conditions. Ohm's law states that the current intensity through a conductor is determined by two factors, the voltage across the conductor and the resistance of the conductor.V Kirchhoff's LawKirchhoff's law includes the first law and the second law. They are the basic laws that are indispensable for the analysis and calculation of complex circuits.5.1 Concepts • BranchA two-terminal element connected in a circuit is a branch. Usually a certain current flows through the branch. (This definition is not universal. For example, if two components are connected in series and then connected in a circuit, it can only be regarded as a branch.)• NodeThe connection point between the branch and the branch is called a node. Usually the current diverges at the junction.• Loop loopA closed path formed by branches is called a loop.Figure9. 6 elements, 6 branches, 4 nodes, 3 independent circuits5.2 Kirchhoff's First Law (Nodal Current Law)The textual expression of KCL: For any node, the algebraic sum of the current flowing into (or out of) the node is equal to zero.Its mathematical expression:The regulation of current positive and negative: Generally, the current flowing into the node is positive, and the current flowing out of the node is negative.The physical meaning of KCL: conservation of chargeNote: KCL is not only applicable to a node, but also to a part of the circuit, as shown in the shaded part of the above figure:i3＝i65.3 Kirchhoff's Second Law (Law of Loop Voltage)KVL’s literal expression: In any closed loop of the circuit, go around a circle in a certain direction, and the algebraic sum of the voltage of each segment is zero.That is: or. When applying the law of loop voltage, the electromotive force is often written on the left side of the equation, and the voltage is written on the right side of the equation.The method for determining the sign of each electromotive force and voltage in the second expression is as follows:① First select the current direction of each branch.② Any choice of the detour direction along the loop (clockwise or counterclockwise).③ If the direction of the current flowing through the resistor is the same as the detour direction, the voltage drop on the resistor is positive, otherwise, it is negative.④ If the direction of the electromotive force is the same as the direction of the orbit, the electromotive force is positive, otherwise, it is negative.The physical meaning of KVL: energy conservation.5.4 Application Note of Kirchhoff's Law• Kirchhoff’s law is a general law that the circuit should satisfy, and has nothing to do with the specific properties of the components;• Kirchhoff’s law applies to any lumped circuit, that is, nonlinear, time-varying circuits, etc.;• Application steps:A. Divide the branch roads and number them;B. Specify the branch current and voltage reference direction, and generally need to be associated;C. Select the appropriate node according to the meaning of the question, and apply KCL;D. Or choose the appropriate circuit according to the meaning of the question, apply KVL, and pay attention to independence.Example: Use KVL to derive the relationship between the total resistance and the sub-resistance and the voltage division formula in the series resistance circuit.Apply KVL according to the current and voltage reference direction and the detour direction of the loop calibrated in the figure:-u+u1+u2+…+un = 0 or u=u1+u2+…+un Because the voltage and current of each resistor obey Ohm's law: uk=iRk, there are:u = i × R1 + i× R2 +...... +i× Rn = i× ( R1+R2+…+Rn)= i Re among them: Re=R1+R2+…+Rn, which is the total resistance or equivalent resistance.uk = iRk=( u/Re ) Rk, which is the voltage division formula of the series circuitVI Series and Parallel Circuit Identification MethodsMethod 1: Current flow method(1) Starting from the positive pole of the power supply, use arrows to mark the path of the current along the connected wires, and finally return to the negative pole of the power supply;(2) Observe whether the current has a shunt and confluence point:If there is only one path for the current in the circuit, the components are connected in series (as shown in Figure a below);If there is a shunt point and a confluence point in the circuit, that is, the direction of the current is greater than one path, the components between the shunt point and the confluence point are connected in parallel (as shown in Figure b below)Figure10. Current flow methodMethod 2: Demolition methodRemove any electrical appliances:If the other electrical appliance cannot work, the two electrical appliances are connected in series (as shown in Figure a below)If the other consumer still works without being affected, the two consumers are connected in parallel (as shown in Figure b below)Figure11. Demolition methodMethod 3: Node MethodFor other non-intuitive non-series circuits, the situation is more complicated and needs to be judged according to several steps:The first step is to mark nodes. That is, use different letters (or symbols) to mark all nodes of the circuit. As shown in the following figure (a), the four points A, B, C, and D are all nodes in the circuit.The second step is to merge the nodes. According to the characteristics of the nodes, some of the nodes you have marked may be equivalent to the same node. The letters (or symbols) belonging to the same node must be changed to the same letter (or symbol), as shown in the circuit shown in Figure (a) Point A and point C are the same node, C should be changed to A, point B and point D should be the same node, D should be rewritten as B, that is to say, the circuit shown in Figure (a) essentially has two nodes A and B .Figure12. Node MethodThe third step is to determine the connection mode of the circuit. There are usually two ways to judge:Method one:Direct judgment: as shown in the figure (a) above, both ends of the resistors R1, R2 and R3 are independently connected to nodes A and B, so R1, R2 and R3 are connected in parallel.Method Two:Drawing judgment: that is, draw the intuitive equivalent circuit diagram of the original diagram. The specific drawing method of the intuitive equivalent circuit diagram of the circuit diagram in Figure (a) is: first determine the two points A and B on the paper, and then combine the original diagrams A and B. The components between the two points B are independently connected to the newly determined points A and B, as shown in the above figure (b), that is, the equivalent circuit diagram of figure (a) is figure (b).Warm reminder: The "node method" is generally used to identify irregular and more complex circuits, which has certain difficulties. There are many ways to identify series and parallel circuits, but you can choose the most suitable method according to your own understanding of the method when using it.VII QuizThe voltage dropped across the 300 ohm resistor isA. 6V B.9V C.2V D.30VAnswer: AⅧ FAQ1. What is the difference between two resistors connected in series, and two resistors connected in parallel?When resistors are in series then net resistance is the sum of individual resistances whereas in parallel it is the sum of the reciprocal of individual resistances.When a resistor is in series the current is the same through all resistors but the voltage is different. The sum of the voltage drop across each resistor is equal to the voltage across a resistor connected in series.When the resistor is in parallel the voltage across each resistor is the same while the current through each resistor is different.In series, the net resistance is higher (sum of each resistance) while in parallel net resistance is lower (net resistance is lower than smallest resistance connected in parallel). 2. Why are resistors connected in series and parallel?Connecting resistors in series increase their total resistance and the power they can handle by distributing the applied voltage. The current flow is the same for each resistor regardless of its resistance.Connecting resistors in parallel reduce their total resistance while at the same time increasing their power they can handle by sharing the current flow in the circuit. The voltage drop across each resistor is the same regardless of its resistance. 3. What is the difference between resistors in parallel and resistors in a series?For resistors in parallel, the voltage across them is the same while the current is the sum let take a case of two resistors connected in parallel the formula 1/Req=1/R1+1/R2 further simplify Req=R1*R2/(R1+R2)While for resistors in series their current is the same but the voltage is the sum and let still take the case of two resistors connected in series to obtain their equivalent Req= R1+R2. 4. How are resistors added in series and parallel?When resistors are connected one after each other this is called connecting in series. This is shown below. To calculate the total overall resistance of a number of resistors connected in this way you add up the individual resistances. This is done using the following formula: Rtotal = R1 + R2 +R3 and so on. 5. Why is resistance different in series and parallel?When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower. Each resistor in parallel has the same full voltage of the source applied to it, but divide the total current amongst them. 6. How do you calculate resistors in parallel?Parallel Resistor EquationIf the two resistances or impedances in parallel are equal and of the same value, then the total or equivalent resistance, RT is equal to half the value of one resistor. That is equal to R/2 and for three equal resistors in parallel, R/3, etc. 7. Why is resistance less in parallel?When resistors are connected in parallel, more current flows from the source than would flow for any of them individually, so the total resistance is lower. 8. How do you sum resistors in parallel?The sum of the currents through each path is equal to the total current that flows from the source. You can find total resistance in a Parallel circuit with the following formula: 1/Rt = 1/R1 + 1/R2 + 1/R3 +... If one of the parallel paths is broken, the current will continue to flow in all the other paths. 9. What happens when you add a resistor in series?When resistors are connected in series, the total voltage (or potential difference) across all the resistors is equal to the sum of the voltages across each resistor. ... In other words, the voltages around the circuit add up to the voltage of the supply. 10. What is the difference between series connection and parallel connection?A parallel circuit refers to a circuit with two or more two paths for the current to flow. ... In a series circuit, all the components are arranged in a single line. In a parallel circuit, all the components are arranged parallel to each other.