Question

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

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

Answer 1

Answer: (B), (C)

$L=1\mu HC=\mu FR=1k\Omega$
Inductive reactance $X_L=\omega L$
Capacitive reactance $X_C=\frac{1}{\omega c}$
(A) at $\omega \to 0$
$X_L\to 0$
$X_C\to \infty$
$i\to 0$
(B) at $\omega >>10^6$
$X_L>X_C$
Circuit behaves as inductor.
(C) Current $\&$ voltage are in same phase if $X_L=X_C$
$f=\frac{1}{2\pi \sqrt{LC}}$
which is independent of $R$.
(D) Resonance frequency $\omega =\frac{1}{\sqrt{LC}}=10^{6}rad/s$.