First slide

Power in a.c. circuit

Question

In an LR-circuit, the inductive reactance is equal to the resistance R of the circuit. An e.m.f. E = Eo Cos(ωt) applied to the circuit. The power consumed in the circuit is

Moderate

A

$\frac{{E_0^2}}{R}$
B

$\frac{{E_0^2}}{{2R}}$
C

$\frac{{E_0^2}}{{4R}}$
D

$\frac{{E_0^2}}{{8R}}$

Solution

$P = {E_{rms}}{i_{rms}}\cos \varphi = \frac{{{E_0}}}{{\sqrt 2 }} \times \frac{{{i_0}}}{{\sqrt 2 }} \times \frac{R}{Z}$
$Given\,\,{X_L} = R\,\,so,\,\,Z = \sqrt 2 R \Rightarrow \,P = \frac{{E_0^2}}{{4R}}$

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