Question 364: AC fundamentals

Question

In a $$L$$-$$R$$ circuit the inductive reactance is equal to the resistance $R$ in the circuit. An emf $$E=E_0 \cos \omega t$$ is applied to the circuit. The power consumed in the circuit is

Accepted Answer

Given, inductive reactance $$=R$$
Power consumed $$=E_{\mathrm{rms}} I_{\mathrm{rms}} \cos \phi$$
$$\begin{aligned}
& =\frac{E_0}{\sqrt{2}} 	imes \frac{I_0}{\sqrt{2}} 	imes \frac{R}{Z} \quad\left(\because \cos \phi=\frac{R}{Z}ight) \
& =\frac{E_0}{\sqrt{2}} 	imes \frac{E_0}{Z \sqrt{2}} 	imes \frac{R}{Z} \quad\left(\because I_0=\frac{E_0}{Z}ight) \
& =\frac{E_0^2 R}{2 Z^2} \quad\left(\because X_L=R \Rightarrow Z=\sqrt{2} Right) \
& =\frac{E_0^2}{4 R}
\end{aligned}$$

Answer

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

Answer

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

Answer

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

Answer

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

AC fundamentals

In a $L-R circuit the inductive reactance is equal to the resistance R in the circuit. An emf E=E_0 \cos \omega t$ is applied to the circuit. The power consumed in the circuit is

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