$\text{ If }{\mathrm{E}}_0=200\mathrm{V},\mathrm{R}=25\mathrm{\Omega },\mathrm{L}=0.1\mathrm{H}$ and $C={10}^{-5}$ and let the frequency is variable. Then what is the current at f= 0 and f: = ∞ respectively?

The inductive reactance

$\left(X_L\right)=\omega L=2\pi fL$

The capacitive reactance

$\left(X_C\right)=\frac{1}{\omega C}=\frac{1}{2\pi \mathrm{fC}}$

Impedance of the circuit,

$Z=\sqrt{R^2+{\left(X_L-X_C\right)}^2}$

$\Rightarrow I=\frac{V}{Z}=\frac{V}{\sqrt{R^2+{\left(X_L-X_C\right)}^2}}$

At f = 0,

$X_L=0,X_c=\mathrm{\infty }\Rightarrow Z=\mathrm{\infty }$

$\begin{array}{r}\Rightarrow I=0\\ \text{ At }f=\mathrm{\infty }\end{array}$

$\begin{array}{r}{X}_L=0,X_c=\mathrm{\infty }\Rightarrow Z=\mathrm{\infty }\\ \Rightarrow I=0\end{array}$

In both the cases, Current is 0.