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Introduction to Basic Capacitors Uncertainty in Electronics

  • Contents

Introduction

A Capacitor is a component that can store and release electricity, and it is also one of the most commonly used electronic components. Its distinguishing feature is the "Pass Alternating Current (AC), Stop Direct Current(DC)". In a DC circuit, a capacitor is equivalent to an open circuit. Based on this, we will have this question: What the differences betwen ac and dc capacitors? or Are ac and dc capacitors interchangeable? What's the difference between batteries and capacitors? or Why can't we use capacitors instead of batteries? As for capacitor calculations, what the time constant for discharging a capacitor? Here you will get the answers.

capacitor symbol

Figure 1. Capacitor Symbol

Catalog

Introduction

Ⅰ Why Can the Battery (DC) Charge the Capacitors?

Ⅱ DC Capacitors vs AC Capacitors

Ⅲ Battery or Capacitor?

Ⅳ Calculate the Time Constant for the Discharge of the Capacitors?

Ⅴ FAQ


Ⅰ Why Can the Battery (DC) Charge the Capacitors?

In circuit analysis, there are two types of circuit responses: zero-input response and zero-state response. The so-called zero input response means that the input signal is zero; the so-called zero-state response means that the states of all energy storage components and various power supplies in the circuit are zero.
When analyzing the zero-state response, short-circuit the voltage source and open the current source. For the capacitor, at the moment of energization in the zero state response, it can be considered as a voltage source with zero voltage, so it is equivalent to a short circuit. Analyze the following figures: Figure one is the circuit structure: power supply E, internal resistance r, switch QF, capacitor C and resistance R. When the switch QF is turned on, let's take a look at the current Ic and voltage Uc flowing through the capacitor:

zero input response and zero-state response curve

Figure 2. Zero-input Response and Zero-state Response Curve

We see that at the moment t=0, the current flowing through the capacitor is the largest. The capacitor at this time is equivalent to a voltage source with zero voltage, and the power source E must be charged to it through the internal resistance r. Therefore, we can understand that it is actually a short circuit, so the maximum charging current, that is, the charging current Icmax at t=0 is: Icmax. In the figure, we can see that after 5τ, the current has been zero and the voltage has been charged to almost E. After that, the current flowing through the capacitor will not change any more, and the capacitor at this time plays a role in isolating the direct current. As can be seen in the figure, the charging process of the capacitor is divided into two parts, one is the transient transition process, and the other is the steady state process.
Next, analyze the transition process carefully. Let us first look at the opportunity RC of the resistance r and the capacitance C. Resistance is equal to voltage divided by current, and capacitance is equal to electricity divided by voltage, and electricity is equal to current divided by time, so there is: RC, here T is called the time constant, generally represented by τ.
The current thus flowing through the capacitor is: Ic
The exponential function here, its exponent is equal to the ratio of time to the time constant, so it is a pure number. When the time is equal to 0, Ic=Icmax; when the time is equal to 5τ, the value of the exponential function is 6.738×10-3. After substituting the above formula, get the current at this time is: current I
At this time, the expression of the capacitor voltage Uc is: Uc
Note: Theoretically, the voltage on the capacitor should be charged to ER/(R+r), but because in the steady state, the impedance of the capacitor is infinite, so its voltage can be charged to E.
From here we can see that the so-called capacitor blocking DC actually refers to its steady-state characteristics. In the steady state, the equivalent impedance of the capacitor is infinite, and the DC current cannot pass through it, so the current is zero, and there is a very small leakage current at most. In the transient state, the capacitor can flow current, and in the initial stage since the current is similar to a voltage source due to the capacitance, its characteristic is almost a short circuit, so the initial value of the current is the maximum.

If our power source is not a battery, but a square wave pulser, what is the voltage of the resistor R after the capacitor?

square wave pulser

Figure 3. Square Wave Pulser

The Figure 3. is a case where the time constant is small, which reflects the impulse response of the capacitor; and the picture below is a case where the time constant is large, which reflects these two effects have a large number of applications.

If our power supply is AC, what is the voltage on the resistor R after the capacitor?
When discussing the response of the capacitor to the AC current range, we need to temporarily look back at the first picture. From the figure, we can see that when the current takes the maximum value, the voltage is the minimum value, however, when the current takes the minimum value, the voltage is the maximum value. Why is that?
The capacitance is equal to the ratio of the electric quantity to the voltage, that is, C=Q/U=It/U, from which the current is obtained: I=CU/t. And the voltage Uc on the capacitor is actually constantly changing. It is a function of time, so the above formula can be written as: capacitor I
This formula is very important, it is the key to unlock the capacitor under the action of AC power.
The AC voltage can be expressed as, put it into the expression of the capacitor current capacitor voltage, and get: Ui
We can see that when the voltage is zero, the current has reached its maximum value. In other words, for an AC power supply, the current I flowing through the capacitor leads the voltage by 90 degrees. It reveals the expression form of capacitance under AC voltage.
Capacitors are used to block direct current, but they only have this performance in steady state. When the DC power supply changes rapidly, that is, the power supply continuously changes from zero to the maximum value, and becomes zero again. In this cycle, we can see that the capacitor not only does not block the DC, but becomes a component with almost zero impedance.
In fact, it can be known from the capacitive reactance (Xc) that when the frequency of the power supply increases, the capacitive reactance of the capacitor decreases linearly with the increase in frequency. When we charge the capacitor with a DC power supply enough, the charging voltage of the capacitor can reach the same level as the electromotive force of the power supply. Here the key is that the capacitor is an energy storage element.

capacitors

Figure 4. Various Capacitors

Ⅱ DC Capacitors vs AC Capacitors

1) Whether DC capacitors and AC capacitors are polarized: AC capacitors are also called non-polarized capacitors. As can be seen from the literal meaning, it can be polarity-independent. So it can be used in AC and DC circuits. The DC current uses a polarized capacitor, which has a high capacity, and a relatively small withstand voltage. In addition, both of them will be lost over time.
2) The mobility of DC capacitors and AC capacitors are different: the voltage at one end of the DC capacitor is always high, and the current will always be the same and flow in one direction. While the two lines from the AC capacitor power supply, their voltage level is changing, so that the current can flow from A to B, or from B to A, and make certain adjustments and changes over time.
3) Direct current and alternating current are different in direction conversion: alternating current can be regarded as two groups of direct current in turn to exert an effect on the load, which can be understood as the vector sum of the two groups of direct current in different time periods. The alternating current can be understood as a group of direct current in one direction in a short enough time.

ceramic capacitors

Figure 5. Ceramic Capacitors

Ⅲ Battery or Capacitor?

Capacitors and batteries are both electrical components, and both are energy storage components. But battery and capacitor are two completely different concepts. The difference between them is:
1) Chemical Energy vs Electrical Energy
The battery stores chemical energy, and then converts it into electrical energy to output. Capacitors store electrical energy, which depends on the two plates to determine the capacity. The former is a chemical change, the latter is a physical change. The main physical feature of a capacitor is to store electric charge, which can be charged and discharged like a battery, but does not undergo a chemical reaction.
2) Capacity
Batteries store a lot of electrical energy, but capacitors store less.
3) Charge and Discharge

charge and discharge curve

Figure 6. Charge and Discharge Curve

The charging and discharging speed and the number of times are different. Generally, it only takes a few seconds or minutes to charge a capacitor, while a battery usually takes several hours. The number of charging and discharging of the capacitor is at least tens of hundreds to thousands of millions of times, and the battery is generally only a few hundred to a thousand times.
4) Functions
The purpose of the two is different. Capacitors can be used for coupling, blocking, filtering, phase shifting, RC, LC resonance and as energy storage components for instantaneous large current discharge. The battery is only used as a power source.

Replacing Bike Battery with Capacitor

Ⅳ Calculate the Time Constant for the Discharge of the Capacitors?

Let’s review the calculation formula for the charge and discharge time of the capacitor. Suppose there is a power supply that charges the capacitor C through the resistor R, V0 is the initial voltage value on the capacitor, Vu is the voltage value after the capacitor is fully charged, and Vt is the voltage value at any time t On the capacitor, then the following calculation formula can be obtained:
Vt = V0 + (Vu – V0) * [1 – exp( -t/RC)]
If the initial voltage on the capacitor is 0, the formula can be simplified to:
Vt = Vu * [1 – exp( -t/RC)]...Charging formula
It can be seen from the above formula that because the index value can only be infinitely close to 0, but it will never be equal to 0, it takes infinite time for the capacitor to be fully charged.
🔺When t = RC, Vt = 0.63Vu
🔺When t = 2RC, Vt = 0.86Vu
🔺When t = 3RC, Vt = 0.95Vu
🔺When t = 4RC, Vt = 0.98Vu
🔺When t = 5RC, Vt = 0.99Vu
It can be seen that after 3~5 RCs, the charging process is basically over. When the capacitor is fully charged, the power supply is short-circuited, and the capacitor C will be discharged through R. At any time t, the voltage on the capacitor is:
Vt = Vu * exp( -t/RC)...Discharging formula

 

Ⅴ FAQ

1. Can you use a capacitor as a battery?
A voltage applied across the conductors creates an electrical field in the capacitor, which stores energy. A capacitor operates like a battery in that, if a potential difference is applied across it that can cause a charge greater than its "present" charge, it will be charged up.

 

2. Why can't we use capacitors instead of batteries?
Capacitors don't provide large amount of energy because they have less energy density than batteries. Capacitors are useful to provide short duration power requirements because they can be charged or discharged at a higher rate than the batteries.

 

3. What is the difference between a battery and supercapacitor?
Differences Between Capacitor and Battery
Batteries excel at storing energy, while supercapacitors rate better for power. In practical terms, this means that supercapacitors are better at discharging their stored energy quickly, while batteries save more energy in the same amount of material.

 

4. Which is better battery or capacitor?
A capacitor is able to discharge and charge faster than a battery because of this energy storage method also. ... However, in general batteries provide higher energy density for storage, while capacitors have more rapid charge and discharge capabilities (greater Power density).

 

5. What is discharging of capacitor?
Discharging a capacitor means releasing the charge stored within the capacitor. ... Hence the capacitor current exponentially reaches zero from its initial value, and the capacitor voltage reaches exponentially to zero from its initial value during discharging.

 

6. Is it safe to discharge a capacitor with a screwdriver?
It's often safe to discharge a capacitor using a common insulated screwdriver; however, it is usually a good idea to put together a capacitor discharge tool and use that for electronics with larger capacitors such as household appliances.

 

7. Can you discharge a capacitor with a multimeter?
The multimeter isn't used directly to discharge the stored energy of a capacitor. Instead, people use it to measure the voltage and power of the capacitor to know whether it is fully released or not. You can use different tools such as a light bulb or a DIY discharge tool for the process.

 

8. Why do we need to discharge a capacitor?
You must discharge the capacitors before working on power supply circuits so you won't get shocked. ... Using a screwdriver to discharge the capacitor is not recommended because you can generate a spark and damage the printed circuit board or circuitry of the power supply. You can even blow the power section.

 

9. What is discharging time of capacitor?
RC Discharging Table. Note that as the decaying curve for a RC discharging circuit is exponential, for all practical purposes, after five time constants the voltage across the capacitor's plates is much less than 1% of its inital starting value, so the capacitor is considered to be fully discharged.

 

10. What is the time constant of a capacitor?
The time constant of a series RC (resis-tor/capacitor) circuit is a time interval that equals the product of the resistance in ohms and the capacitance in farad and is symbolized by the greek letter tau (τ). The time in the formula is that required to charge to 63% of the voltage of the source.

 

11. Is the time constant the same for charging and discharging the capacitor?
The time constant of a resistor-capacitor series combination is defined as the time it takes for the capacitor to deplete 36.8% (for a discharging circuit) of its charge or the time it takes to reach 63.2% (for a charging circuit) of its maximum charge capacity given that it has no initial charge.

 

12. What is the formula of discharging of capacitor?
q=ϵC(1−eCR−t) where q is the charge on the capacitor at time t,CR is called the time constant, ϵ is the emf of the battery. Discharging: If the plates of a charged capacitor are connected through a conducting wire, the capacitor gets discharged.

 

13. What is energy stored in capacitor?
Electrical potential energy
Energy stored in a capacitor is electrical potential energy, and it is thus related to the charge Q and voltage V on the capacitor. We must be careful when applying the equation for electrical potential energy ΔPE = qΔV to a capacitor. Remember that ΔPE is the potential energy of a charge q going through a voltage ΔV.

 

14. Where is energy stored in capacitor?
A charged capacitor stores energy in the electrical field between its plates. As the capacitor is being charged, the electrical field builds up. When a charged capacitor is disconnected from a battery, its energy remains in the field in the space between its plates.

 

15. Which type of current is blocked by a capacitor?
Alternating current doesn't really "flow", it just oscillates back and forth. A capacitor acts like an elastic membrane, it allows the oscillation but blocs the flow of DC current.

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