Question

In an L-R circuit, the inductive reactance is equal to the resistance $R$ of the circuit. An emf $E=E_{0}cos\omega t$ 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

The correct option is C $\frac{E_0^2}{4R}$

$\begin{array}{c}PowerConsumed:P=E_{rms}{i}_{rms}\cos \varphi \\ P=E_{rms}\left(\frac{E_{rms}}{Z}\right)\frac{R}{Z}=\frac{{E_{rms}}^{2}R}{Z^2}\\ whereZ=\sqrt{R^2+{X_L}^2}\\ X_L=R\to Z=\sqrt{2}R\\ E_{rms}=\frac{E_o}{\sqrt{2}}\\ Therefore,\\ P=\frac{{E_0}^2}{4R}\end{array}$