Question

Four different circuit components are given in each situation of List 1 and all the components are connected across an ac source of same angular frequency $\omega =200rad{s}^{-1}$. The information of phase difference between the current source voltage in each situation of List 1 is given in List 2. Match the circuit components in List 1 with the corresponding List 2.

Answer 1

$\left(A\right)$ Its RC circuit therefore, current leads the voltage by a phi.
$\tan \varphi =\frac{(X_L-X_C)}{R}$
$\tan \varphi =-\frac{1}{\omega CR}=\frac{1}{200\times 500\times {10}^{-6}\times 10}=1$
$\varphi =-\frac{\pi }{4}$
Therefore$,2\&3$
(B)Pure inductor, phase difference must be $\pi /2$
and currents lags the voltage therefore$,1\&4$
(C)LC circuit phase difference$=\frac{\pi }{2}$
$X_L-X_C=\omega L-\frac{1}{\omega C}$
$X_L-X_C=200\times 4-\frac{1}{200\times 3\times {10}^{-6}}$
$X_L-X_C=800-\frac{1000000}{600}$
$X_L-X_C=800-\frac{10000}{6}<0$ therefore,phase is $-\frac{\pi }{2}$
Current leads the voltage
therefore$,1\&3$
$\left(D\right)$ L-R circuit
$\tan \varphi =\frac{X_L}{R}$
$\tan \varphi =\frac{\omega L}{R}$
$\tan \varphi =\frac{200\times 5}{1000}=1$
Therefore, $\varphi =\frac{\pi }{4}$
Since L-R therefore, current lags voltage.
Therefore$,2\&4$