# AC Voltage Capacitors

View Notes

## AC Voltage

This article gives a clear knowledge of electric circuits when one uses an AC voltage across a capacitor. In this circuit layout, we have linked a capacitor and an AC voltage V, represented by the symbol “~.”

The voltage in the circuit produces a potential difference across its terminals that varies sinusoidally.

The expression about the potential difference v, or the AC voltage is given below:

v = vmsin⁡ωt

Where,

vm = amplitude of the oscillating potential difference

ω = angular frequency

We can calculate the current that is available in the resistor of the present voltage by using the Kirchhoff’s loop rule.

Here is the expression of the Kirchhoff’s loop rule:

$\sum$v(t) = 0

The diagram provided above explains the AC Voltage source applied across a Capacitor.

### Capacitance in AC Circuit and Capacitive Reactance

In the above figure, we can write an expression for the capacitor:

v = $\frac{q}{C}$

As mentioned earlier about v, we can rewrite the expression as:

vmsin⁡ωt = $\frac{q}{C}$

We can calculate the amount of current through the circuit by using this relation,

i = $\frac{dq}{dt}$

⇒ i = $\frac{d(v_{m}Csinωt)}{dt}$ = ωCvmcos ωt

⇒ i = $i_{m}sin(ωt +\frac{π}{2})$

In the above expression, a relation is used which is Cosωt = $sin(ωt +\frac{π}{2})$

Also, we can rewrite the amplitude of the current as:

im = ωCvm

Or, we can express it as

im = $\frac{v_{m}}{\frac{1}{ω_{C}}}$

In this expression, $\frac{1}{ω_{C}}$ can be taken as the equivalent to the resistance of the device.

This is why the term for this expression is said to be the capacitive resistance. XC is the symbol used for the captive resistance.

XC = $\frac{1}{ω_{C}}$

Also, we can calculate the amplitude of the current in the circuit by using the following relation:

im = $\frac{v_{m}}{X_{C}}$

### How Does a Capacitor Work in AC Circuit?

In an electric circuit, a capacitor puts a direct linkage with the AC supply voltage. When there is an alteration in the supply voltage (voltage increases or decreases), then the capacitor gets charged or discharged by following the change in voltage.

When current passes through the circuit, it will follow one direction, and then in the other direction without letting any actual current to pass through the capacitor.

However, in a DC circuit, the scenario is different. When current flows through a capacitor which is linked with the DC circuit, the capacitor plate possesses both positive and negative charge.

### AC Capacitor Circuits

When a capacitor is linked with an AC circuit, it will consecutively charge and discharge at a rate calculated by the frequency of the supply. In AC circuits, capacitance varies with frequency as the capacitor is being charged and discharged constantly.

### What is the Role of Capacitor in AC and DC Circuit?

1. Role of a Capacitor in DC circuit

In a DC (direct current) circuit, a capacitor gets charged up at a slower rate. A capacitor gets charged up to its supply voltage but opposes the further passage of current through it. It blocks the current flow as the dielectric of a capacitor is non-conductive and an insulator.

2. Role of a Capacitor in AC circuit

When a capacitor is used in an AC circuit, it charges and discharges to change the supply voltage. According to the record, the current becomes directly proportional to the voltage rate at its greatest, across the plates.

The capacitors that are linked in an AC circuit blocks the power supply when they are fully charged. When there is an AC power supply in the circuit, the capacitors will charge and discharge alternatively at a rate determined by the supplied frequency.

### Function of Capacitor in AC Circuit

We know that capacitors are used to store energy on their conductive plates in the form of an electrical charge.

1. Capacitors are used to buildup voltage above the input voltage. It helps in the smooth current fluctuations.

2. Most importantly, capacitors are used in rectifier circuits to level the current fluctuations.

3. Capacitors are also used to block the DC static voltage and allow AC signals to pass from one circuit area to another. These types of capacitors are known as coupling capacitors.

4. To eliminate any AC signal at the DC bias point, decoupling capacitors are used.

5. The starting torque can be improved through capacitors. Also, capacitors are good to go in the single phase.

6. Also, capacitors are used to improve the power factor in power systems.

### AC through Capacitor Derivation

We can name a pair of conductors as a capacitor, separated by some medium. When we link a capacitor with an AC circuit, we can find the current flowing through it.

When we connect a lamp in that circuit, the lamp glows, which shows the current passage in the AC circuit. We concluded that a capacitor is a conductor in the AC circuit, but works as an insulator in the DC circuit.

Q1. Can capacitors store AC?

Ans: Yes, capacitors can store alternating current. The capacitor can restore the AC as AC converses the direction on a steady source. This makes the capacitor charged alternatively like charging, discharging, and then charging in the reverse direction.

Q2. Provide some ways to find the max voltage across a capacitor.

Ans: There is a notation on the capacitors, and the maximum voltage for a capacitor lies between 1.5V to 100V. The capacitor has certain endurance power to handle a maximum voltage.

For finding the voltage across a capacitor, the formula is VC = Q/C.

Here,

Q = Amount of charge stored on each plate

C = The capacitance

Q3. What is the working voltage of a Capacitor?

Ans: The working voltage of a capacitor can be defined as the maximum continuous voltage applied across the capacitor and void of any failure during the working life in either DC or AC circuit. In short, the working voltage of a capacitor in a DC circuit is named WVDC. You must find the value of the WVDC printed on the side of a capacitor.

Q4. Can Capacitors reduce voltage?

Ans: Yes, the capacitor can help in reducing the voltage. For this, you must use a voltage Dropping Capacitor in series with the phase line. This is the easiest and time-saving method, can be availed at cost-effective pricing.