Question

Sol. [Key Concept: Series LCR — current amplitude I₀ = V₀/Z]

Angular frequency of $AC$ source, $\omega = 2 \times 10^{3}rad/s$

$$\begin{matrix} & \text{~}\text{Inductive reactance,}\text{~}X_{L} = \omega L = \left( 2 \times 10^{3} \right)_{\times}\left( 10 \times 10^{- 3} \right) = 20\Omega \\ & \text{~}\text{Capacitive reactance,}\text{~}X_{C} = \frac{1}{\omega C} = \frac{1}{\left( 2 \times 10^{3} \right)_{\times}\left( 25 \times 10^{- 6} \right)} = 20\Omega \\ & \text{~}\text{Impedance}\text{~}Z\text{~}\text{for circuit}\text{~} = R\left( \because X_{L} = X_{C} \right.\ \text{~}\text{and circuit is at resonance)}\text{~} \\ & \ \therefore\text{~}\text{current amplitude,}\text{~}i_{0} = \frac{V_{0}}{Z} = \frac{V_{0}}{R} = \frac{220}{100} = 2.2\text{ }A \end{matrix}$$