Capacitors in A.C.

DC Capacitor - Recap 

A Capacitor is a device for storing Electrical Charge. A Capacitor consists of two parallel plates separated by an insulator. The symbol for a Capacitor is shown below:-

Once connected within the circuit, negative charge builds up on one of the electrodes, causing a positive charge to build up on the other electrode. This causes Energy to be stored between the plates. 

Current in AC Circuits

For the vast majority of Electrical components, the Frequency of an AC supply will have no effect on them. For example, the circuit below shows a resistor connected to an AC supply :-

In the above circuit, if the Frequency of the the AC Supply is altered, the following graph will be plotted :-

As can be seen from the above graph, for a Resistor (and most other components) the Frequency of the supply and the Current are independent of each other. 

There are two exceptions to this, however, Capacitors and Diodes. 

AC Current through a Diode 

In a Diode, the Current can only flow in one direction, giving a very different graph :-

As can be seen above, the Voltage switching creates a Current flow when the Diode is forward-biased, then a zero value when the Diode is reversed-biased. 

AC Current through a Capacitor 

If the Capacitor is connected to an AC supply, unlike DC, the charging of the Capacitor does not occur. This is because the constantly alternating supply will continuously switch between charging and discharging each plate.  For example, the circuit below shows a Capacitor connected to an AC Supply:-

The physical explanation of how a Capacitor affects an AC Circuit requires a detailed understanding of the flow of charges within the circuit. 

AC Period > Charge time of Capacitor 

If the time taken for the AC signal to alternate is longer than the time to fully charge the capacitor, the following current graph will be generated :-

Each step of the charging cycle follows the below steps :-

As soon as the Capacitor starts to charge, there is a large Current within the circuit. 

As the Charge builds up on the Capacitor, the Potential Difference between the plates of the Capacitor and the Power supply becomes smaller.

When the Capacitor is fully charged, the P.D. between the Power supply and the plates of the Capacitor is zero, and no more Current flows. 

Note - The discharge process is identical to above, except the Current flow is in the opposite direction. 

As can be seen above, depending on how much longer the period is than the charge time, the circuit can spend a lot of time with no Current flowing. 

AC Period < Charge time of Capacitor 

If the AC Period is less than the Charge time, however, the Capacitor would not have enough time to charge or discharge fully, meaning that a Current would always be flowing. 

As the Current is at its maximum value as soon as the switch occurs, then reduces exponentially, the faster the alternation, the higher the average current will be. 

This is shown graphically below...

Low Frequency AC Supply :-

High Frequency AC Supply :-

If the Frequency of the the AC Supply is altered, the following graph will be plotted :-

As can be seen from the above graph, for a Capacitor, the Frequency of the supply and the Current are directly proportional to each other. 

Capacitive Reactance 

In the above circuit, there was also a Voltmeter across the Capacitor. If the Current and Voltage are measured in this way, it can shown for a constant Frequency that the relationship V / I is equal to a constant value. This constant gives a value for the opposition to the flow of Current within the Capacitor circuit. 

In a Capacitor Circuit, this opposition to Current Flow is known as 

the Capacitive Reactance (Xc), and is the equivalent of  Resistance in Ohm's Law.  

Note - The Capacitive Reactance does have the unit of Ohms (Ω) but we do not refer to this as Resistance. 

It can be shown that the Capacitive Reactance, Capacitance and Frequency of an AC signal are related in the following formula :-

Where :-

Xc  =  Capacitive Reactance (Ω) 

f  =  Frequency of the Alternating Signal (Hz) 

C  =  Capacitance of the Capacitor (F)