Question

In the following circuit, the potential of source is $E_0=200$ volts, $R=200\Omega$, $L=0.1$ henry, $C=10.6$ farad and frequency is variable, then the current at f=0 and f=$\infty$ is :

• A. 0A, 10A
• B. 10A, 0A
• C. 10A, 10A
• D. 0A, 0A

Answer 1

The correct option is D 0A, 0A

$Z=\sqrt{R^2+(\omega L-\frac{1}{\omega C}{)}^2}$

$I=\frac{V}{Z}=\frac{V\omega C}{\sqrt{R^2+{({\omega }^{2}LC-1)}^2}}$

when $w\to 0$ then

$I=\frac{V\omega C}{\sqrt{R^2+1^2}}$ $\Rightarrow I\to 0$

or when $w\to \infty$,

$R^2+{({\omega }^{2}LC-1)}^2\to \infty or$
$\frac{1}{\sqrt{R^2+{({\omega }^{2}LC-1)}^2}}\to 0$
$\Rightarrow I\to 0$

therefore, current is zero in both case.