Question 325: AC fundamentals

Question

An e.m.f. $E=E_0 \cos \omega t$ is applied to the $L-R$ circuit. The inductive reactance is equal to the resistance ' $R$ ' of the circuit. The power consumed in the circuit is

Accepted Answer

$$
\begin{aligned}
& P=E_{r m s} I_{r m s} \cos \phi \
& \cos \phi=\frac{R}{Z} \
& 	ext { Also, } I_{m s}=\frac{E_{m s}}{Z}=\frac{E_0}{Z \sqrt{2}} \
	herefore \quad & P=\frac{E_0}{\sqrt{2}} 	imes \frac{E_0}{Z \sqrt{2}} 	imes \frac{R}{Z} \
& =\frac{E_0^2 R}{2 Z^2} \quad	ext{.... (i)}\
& \quad 	ext { Given } X_L=R \
	herefore \quad & Z=\sqrt{R^2+R^2}=\sqrt{2} R \
	herefore \quad & P=\frac{E_0^2}{4 R}\quad	ext{... [From (i)]}
\end{aligned}$$

Answer

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

Answer

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

Answer

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

Answer

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

AC fundamentals

An e.m.f. E=E_0 \cos \omega t is applied to the L-R circuit. The inductive reactance is equal to the resistance ' R ' of the circuit. The power consumed in the circuit is

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