$$\require{cancel}$$

# 13.2: Alternating Voltage across a Capacitor

 FIGURE XIII.3
 +
 -

At any time, the charge Q on the capacitor is related to the potential difference V across it by    If there is a current in the circuit, then Q is changing, and

Now suppose that an alternating voltage given by

13.2.1

is applied across the capacitor.

In that case the current is                                                                          13.2.2

which can be written                                                                                       13.2.3

where the peak current is                                                                                     13.2.4

and, of course

The quantity 1/(Cw) is called the capacitive reactance XC.  It is expressed in ohms (check the dimensions), and, the higher the frequency, the smaller the reactance.  (The frequency n is w/(2p).)

[When we come to deal with complex numbers, in the next and future sections, we shall incorporate a sign into the reactance.  We shall call the reactance of a capacitor rather than merely , and the minus sign will indicate to us that V lags behind I.  The reactance of an inductor will remain Lw, since V leads on I. ]

Comparison of equations 13.2.1 and 13.2.3 shows that the current and voltage are out of phase, and that V lags behind I by 90o, as shown in figure XIII.4.

 FIGURE XIII.4
 I
 V