Question

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. $\frac{E_{0}^{2}}{8R}$

Answer 1

Answer: (C)

$\frac{E_{0}^{2}}{4R}$

Answer 2

Power consumed $P = E_{rms}i_{rms}\cos\varphi = E_{rms}\left( \frac{E_{rms}}{Z} \right)\frac{R}{Z}$ ⇒

$P = \frac{E_{rms}^{2}R}{Z^{2}};$ where $Z = \sqrt{R^{2} + X_{L}^{2}}$

Given $X_{L} = R$ ⇒ $Z = \sqrt{2}R$ also $E_{rms} = \frac{E_{0}}{\sqrt{2}}$ ⇒ $P = \frac{E_{0}^{2}}{4R}$.