In the circuit shown, L = 1 μ H , C = 1 μ F a n d R = 1 k Ω . They are connected in series with an a.c. source V = V 0 sin ⁡ ω t as shown. Which of the following options is/are correct?

Question

Aicharya · Accepted Answer

The current will be in phase with voltage when phase angle is zero,

$∴ \tan ϕ = \frac{ω L - \frac{1}{ω C}}{R} = 0$

Where $ω, L, C, R$ are the angular frequency, inductance, capacitance and resistance respectively.

$\Rightarrow ω = ω_{0} = \frac{1}{\sqrt{L C}}$

$\Rightarrow ω_{ο}$ is independent of $R$

$\Rightarrow (r e s o n a n t f r e q u e n c y) ω_{0} = 10^{6} r a d / s$

Current in the circuit is given by,

$i_{0} = \frac{V_{0}}{\sqrt{R^{2} + {(ω L - \frac{1}{ω C})}^{2}}}$

When $ω \to 0, i_{0} \to 0$

For $ω ≫ ω_{0}$ circuit behaves as inductor.

In the circuit shown, L = 1 μ H , C = 1 μ F a n d R = 1 k Ω . They are connected in series with an a.c.…

Solution