Looking for classes? Ksquare Career Institute, Bengaluru →
A resistance 'R' draws power 'P' when connected to an AC source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes 'Z', the power drawn will be
A
$P\left(\frac{R}{Z}\right)^2$
B
$P\sqrt{\frac{R}{Z}}$
C
$P\left(\frac{R}{Z}\right)$
D
P
Detailed Solution
With R only: $P = \frac{E^2}{R}$ (rms values)
With L in series: $P' = EI\cos\phi = E\cdot\frac{E}{Z}\cdot\frac{R}{Z} = \frac{E^2R}{Z^2}$
$\frac{P'}{P} = \frac{R^2}{Z^2}$
$P' = P\left(\frac{R}{Z}\right)^2$
With L in series: $P' = EI\cos\phi = E\cdot\frac{E}{Z}\cdot\frac{R}{Z} = \frac{E^2R}{Z^2}$
$\frac{P'}{P} = \frac{R^2}{Z^2}$
$P' = P\left(\frac{R}{Z}\right)^2$