Question

For the given AC RLC circuit, at a particular frequency of the AC source, the current -

• A. Lead the voltage by ${\tan }^{-1}\left(3/4\right)$
• B. Lead the voltage by ${\tan }^{-1}\left(5/8\right)$
• C. Lag the voltage by ${\tan }^{-1}\left(3/4\right)$
• D. Lag the voltage by ${\tan }^{-1}\left(5/8\right)$

Answer 1

The correct option is A Lead the voltage by ${\tan }^{-1}\left(3/4\right)$


Suppose, the AC source voltage is given by,

$V=V_m\sin \left(\omega t\right)$

Then, the AC in the circuit is,

$I=I_m\sin (\omega t+\varphi )$

So,

$\tan \varphi =\frac{X_C-X_L}{R}=\frac{8-5}{4}=\frac{3}{4}$

$\Rightarrow \varphi ={\tan }^{-1}\left(3/4\right)$

Hence, option $\left(A\right)$ is the correct answer.