# Capacitor in AC Circuits

In AC circuits, we will examine the capacitor subject under the heading capacitance and capacitive reactanse.

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When the capacitors are connected to a direct current DC supply voltage, the platescharges until the voltage value on the capacitor is equal to the voltage applied externally.The capacitor will keep this load indefinitely, acting as a temporary storage device as long as the applied voltage is maintained.

During this charging process,An electric current (i) flows into the capacitor, which causes the plates to start holding an electrostatic charge.This charging process is not instantaneous or linear, becausethe power of the charging current is maximum when the capacitor plates are not charged andthe capacitor decreases exponentially over time until fully charged.

This is because the electrostatic field between the plates opposes any changes in the potential difference between the plates at a rate equal to the speed of change of the electric charge on the plates.OneThe ability to store a load on the plates of the capacitor is called capacitance (C).

So that athe capacitor charging current can be defined as follows: i = CdV/dt.When the capacitor is "full charge",when the capacitor becomes saturated, it prevents the flow of more electrons to its plates.However, if we apply alternating current or AC supply,the capacitor alternately charges and discharges at a rate determined by the feeding frequency.Then capacitance in ac circuits,the capacitor changes with frequency as it is constantly charged and discharged.

AWe know that the flow of electrons on the capacitor's plates is directly proportional to the rate of change of voltage between these plates.Then, capacitors in AC circuits, as with AC signals, tend to pass current when the voltage on their plates changes continuously over time, but we can see that it is not destitute to pass current when the applied voltage is at a constant value.

### Capacitor in AC Circuits

In the fully capacitive circuit above,the capacitor is directly connected to the AC supply voltage.As the supply voltage increases and decreases,the capacitor charges and discharges according to this change.We know that the charging current is directly proportional to the voltage change rate (0^{o}-180 during^{that} sine wave) along the plates where the feed voltage switches from positive semi-cycle to negative semi-cycle, or vice versa.

As a result, the lowest voltage change rate occurs when the AC sine wave intersects at the maximum positive peak ( +V _{MAX)} and the minimum negative peak ( -V _{MAX).}In these two positions in the loop, the sinusoidal voltage is constant, so the change rate is zero, so dv/dt is zero, which causes zero current change in the capacitor.So when dv/dt = 0,the capacitor acts as an open circuit, so it becomes i = 0.

At 0^{o,}the change rate of the supply voltage increases in a positive way, resulting in the maximum charging current at that moment.When the applied voltage reaches the maximum peak value of 90^{o}for a very short period of time, the supply voltage neither increases nor decreases, so the current does not pass through the circuit.

When the voltage applied in 180^{o}starts to drop to zero, the capacitor is discharged negatively because the voltage slope is negative.At^{that} point of 180 o along the line, the voltage change rate is again at the maximum, so the maximum current flows at that moment, and so on.

Then, in the AC circuitsFor capacitors, we can say that the instantaneous current is at minimum or zero when the applied voltage is at the maximum, and when the voltage applied in the same way is minimal, the instantaneous value of the current is maximum or peak value.

From the waveform above, we can see that the current directs the voltage by 1/4 loop or 90^{o,} as shown in the vector diagram.Then we can say that in a completely capacitive circuit the alternating voltage leaves the current 90^{o } **lagging**.

We know that the current flowing from capacitance in AC circuits is against the rate of change of the applied voltage, but like the resistors, capacitors offer some kind of resistance to the passing current flow, but in AC circuits this AC resistance in capacitor circuits is known as **reassurance** or, more commonly, capacitive reassurance in capacitor circuits , hence the **capacitance capacitive reactance** in AC circuits.

## Capacitive Reactance

**Capacitive reactas in**a fully capacitive circuit is only against current flow in AC circuits.Like resistance, reassurance is measured in Ohm, but the X symbol is given to distinguish it from a fully resistant value.Since the colorance is an amount that can be applied to capacitors as well as inductors, it is more commonly known as **capacitive reassurance** when used with capacitors.

For capacitors in AC circuits, the Xc symbol is given if capacitively reactive.Then we can actually say that capacitive reassurance is a capacitor resistance value that changes with frequency.In addition, capacitive reactax depends on the capacitance of the capacitor in the Farad, as well as the frequency of the AC waveform, and the formula used to describe capacitive reactance is given as follows:

Here: Frequency in F Hertz, capacitance in C Farad, 2ππ angular frequency can also be expressed as the Greek **letter Omega** , ω, which is used to indicate an angular frequency.

If any of the above capacitive recess formula, **frequency** or **capacitance** is increased, it can be seen that the total capacitive reassurance will decrease.As the frequency approaches infinity, the reassurance of capacitors will decrease to zero, acting as an excellent conductor.

However, as the frequency approaches zero or DC, the coloring of capacitors will increase forever, acting as a very large resistance.This means that capacitive recess is "**inversely proportional"**to the frequency for any given capacitance value.

## Capacitive Reactance Against Frequency

Capacitive reassurance of the capacitor decreases as the frequency opposite it increases, so capacitive reassurance is inversely proportional to the frequency.

In contrast to current flow, the electrostatic load (AC capacitance value) on the plates remains constant as it becomes easier for the capacitor to fully absorb the load change in its plates during each half cycle.

Also, as the frequency increasesthe value of the current flowing from the capacitor increases because the voltage change rate increases along the plates.

Then in DC we can see that a capacitor has infinite reassurance (open circuit), a capacitor at very high frequencies has zero reassurance (short circuit).

## AC Capacitance Question Example 1

When a 4μF capacitor is connected with a feed of 880V, 60Hz, calculate the rms current flowing in an AC capacitive circuit.

In AC circuits, the sinusoidal current passing through a capacitor^{that} directs the voltage up to 90 so varies according to the frequency while constantly charging and discharging by the capacitor applied voltage.Onethe AC impedance of the capacitor is known as **the recess** andMore commonly **capacitive reassurance**is called X_{C,} since we deal with capacitor circuits.

## AC Capacitance Question Example 2

When a capacitor with parallel plates was connected to a 60Hz AC source, it was found to have a recess of 390 ohm.Calculate the value of the capacitor in micro-farce.

This capacitive reactanse is inversely proportional to the frequency and, as we look at in ac capacitance training in the AC Theory section, produces contrast to the current flow around a capacitive AC circuit.