Question

In the circle shown $L=1\mu H$, $C=1\mu F$ and $R=1k\Omega$. They are connected in series with a.c. source $V=V_0\sin \omega t$ as shown. Which of the following option is/are correct?

• A. The frequency at which the current will be in the phase with the voltage is independent of $R$.
• B. At $\omega \sim 0$ the current flowing through the circuit becomes nearly zero.
• C. At $\omega >>{10}^{6}rad.s^{-1}$, the circuit behave like a capacitor.
• D. The current will be in phase with the voltage if $\omega ={10}^{4}rad.s^{-1}$

Answer 1

Answer: (A), (B)

The correct options are
A The frequency at which the current will be in the phase with the voltage is independent of $R$.
B At $\omega \sim 0$ the current flowing through the circuit becomes nearly zero.

$X_L=\omega L,X_C=\frac{1}{\omega C}$

At $\omega \sim 0,X_L\to 0,X_C\to \infty$

therefor current will be nearly Zero.

At $\omega >>{10}^6,X_L>>1,and{X}_C\to 0$

hence the circuit does not behave like capacitor.

At resonance frequency $\left({\omega }_0\right)$ i.e.when $X_C=X_L$ current will be in phase with voltage and frequency is independent of R

resonance frequency ${\omega }_0=\frac{1}{\sqrt{LC}}={10}^{6}rad/s$

hence , the correct option are A and B