Higher Engineering Mathematics, Sixth Edition

176 Higher Engineering Mathematics

pulsate at twice the supply frequency. The areas of the

power curve (shown shaded) above the horizontal time

axis represent power supplied to the load; the small

areas below the axis represent power being returned to

the supply from the inductance as the magnetic field

collapses.

A similar shape of power curve is obtained for an

R–Ccircuit, the small areas below the horizontal axis

representing power being returned to the supply from

the charged capacitor. The difference between the areas

above and below the horizontal axis represents the heat

loss due to the circuit resistance. Since power is dissi-

pated only in a pure resistance, the alternative equations

for power,P=I^2 RR, may be used, whereIRis the rms

current flowing through the resistance.

Summarizing,the average powerP in a circuit

containing resistance and inductance and/or capaci-

tance, whether in series or in parallel, is given by

P=VIcosφor P=I^2 RR (V,I and IR being rms

values).