A series R-C combination is connected to an ac voltage of angular frequency $\omega =500rad{s}^{-1}$. If the impedance of the R-C Circuit is $R\sqrt[ ]{1.25}$ , the time constant (in millisecond) of the circuit is

i. $\to$ c., e.; ii. $\to$ b., c., d., e.; iii. $\to$ a., b.; iv. $\to$ b., c., d., e.

a. In this case, steady state current is zero (I=0) because of the presence capacitor. Entire potential will            be across capacitor in steady state. Hence $V_1=0and{V}_2=V.$

b. In steady state $V_1=0so{V}_2=V.$ Also $V_2$ is proportional to I.

c. $X_L=\omega L=2\pi fL=2\pi \times 50\times 6\times {10}^{-3}=1.885\Omega$

$R=2\Omega$

Since $R>X_L,so\text{\hspace{0.17em}\hspace{0.17em}}{V}_2>V_1$ Here $I\ne 0$

$V_{1}and\text{\hspace{0.17em}}{V}_2$ both are proportional to I.
$X_1-1.885\Omega$

$X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 50\times 3\times {10}^{-6}}1061\Omega$

Hence $X_C>X_L,so V_2>V_1$

$e.X_C=1.061k\Omega ,R=1k\Omega$

$X_C>R,so{V}_2>V_1$