Question

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. $P\left(\frac{R}{Z}\right)$
• B. $P$
• C. $P\left(\frac{R}{Z}\right)^2$
• D. $P \sqrt{\frac{R}{Z}}$

Answer 1

Answer: (C)

Case I : $P=V_{rms}I_{rms}$
$=V_{rms}\times\frac{V_{rms}}{R}$

$P=\frac{V^2_{rms}}{R}\Rightarrow V^2_{rms}=PR$
Case II : Power drawn in LR circuit
$P'=V_{rms}I_{rms}\cos\phi=V_{rms}\times\frac{V_{rms}}{Z}\times\frac{R}{Z}$
$=V^2_{rms}\frac{R}{Z^2}=PR\times\frac{R}{Z^2}$ [Using eqn (i)]

$P'=p\left(\frac{R}{Z}\right)^{2}$