B.3 AVERAGE AND RMS VOLTAGE AND CURRENT

When an alternating current flows, the average current is zero, as illustrated in Figure B.4(a). This means that the average voltage is zero.

I_{a v} = 0 = V_{a v}

(B.6)

Yet the alternating voltage and current do cause heating of a resistance. A current, I_rms_, (called the root-mean-square current, or RMS current) is defined as the DC current that has the same effect as the AC current i(t). It can be shown that for a sine wave:

I_{r m s} = \frac{I_{m a x}}{\sqrt{2}} a n d V_{r m s} = \frac{V_{m a x}}{\sqrt{2}}

(B.7)

For AC currents, the power dissipated in a resistance is calculated in terms of the root-mean-square values. That is:

P = I_{r m s}^{2} R o r P = \frac{V_{r m s}^{2}}{R}

(B.8)

For a sine wave, Equation (B-7) can be written:

P = \frac{I_{m a x}^{2}}{2} o r P = \frac{V_{m a x}^{2}}{2 R}

(B.9)