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

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

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