Q. In an $LR$-circuit, the inductive reactance is equal to the resistance $R$ of the circuit. An $e$.m.f. $E = E_{0}\cos{(\omega t)}$ is applied to the circuit. The power consumed in the circuit is
A) $\frac{E_{0}^{2}}{R}$
B) $\frac{E_{0}^{2}}{2R}$
C) $\frac{E_{0}^{2}}{4R}$
D) $\frac{E_{0}^{2}}{8R}$
Explanation
(c) $P = E_{rms}i_{rms}\cos\phi = \frac{E_{0}}{\sqrt{2}} \times \frac{i_{0}}{\sqrt{2}} \times \frac{R}{Z}$
$\Rightarrow \frac{E_{0}}{\sqrt{2}} \times \frac{E_{0}}{Z\sqrt{2}} \times \frac{R}{Z} \Rightarrow P = \frac{E_{0}^{2}R}{2Z^{2}}$
Given $X_{L} = R$ so, $Z = \sqrt{2}R \Rightarrow P = \frac{E_{0}^{2}}{4R}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.