Question

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. $E=E_{0}cos\left(\omega t\right)$ 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 $\frac{E_0^2}{4R}$

$P=E_{rms}{i}_{rms}cos\varphi =\frac{E_0}{\sqrt{2}}\times \frac{i_0}{\sqrt{2}}\times \frac{R}{Z}\Rightarrow \frac{E_0}{\sqrt{2}}\times \frac{E_0}{Z\sqrt{2}}\times \frac{R}{Z}\Rightarrow P=\frac{E_0^{2}R}{2Z^2}Given{X}_L=Rso,Z=\sqrt{2R}\Rightarrow P=\frac{E_0^2}{4R}$