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 X_{C}. 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 90^{o}, as shown in figure XIII.4.
FIGURE XIII.4 |
I |
V |