Higher Engineering Mathematics

188 GEOMETRY AND TRIGONOMETRY

−

0

+

p

i

v

v

p

i

π

ω

2 π

ω t(seconds)

Figure 18.11

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 dissipated only in a pure resistance, the alterna-

tive equations for power,P=IR^2 R, may be used,

whereIRis the rms current flowing through the

resistance.

Summarizing,the average powerP in a cir-

cuit containing resistance and inductance and/or

capacitance, whether in series or in parallel, is

given byP=VIcosφorP=I^2 RR(V,IandIRbeing

rms values).