Question

In the following $\text{AC}$ circuit the emf of source is $E_0=200\text{V}$, $R=20\Omega$, $L=0.1\text{H}$, $C=10.6\text{F}$ and frequency is variable, then the current at frequency $f=0$ and $f=\infty$ are

• A. $Zero$, $10\text{A}$
• B. $10\text{A}$, $Zero$
• C. $10\text{A},10\text{A}$
• D. $Zero,Zero$

Answer 1

The correct option is D $Zero,Zero$

We know that for $\text{LCR}$ circuit, Impedance is given by

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

When, $f=0$, then

$X_L=\omega L=2\pi fL=0$

And , $X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}=\infty$

Therefore, the impedance of the circuit is infinite at $f=0$ is, $Z=\infty$

When $f=\infty$, then

$X_L=\omega L=2\pi fL=\infty$

And, $X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}=0$

Therefore, the impedance of the circuit is also infinite for $f=\infty$ is $Z=\infty$ .

Hence, the circuit will behave as an open circuit in both the cases.

So, current in both the cases will be $zero$.

Hence, option $\left(D\right)$ is correct.