Question

An air-cored coil having a winding resistance of 10 \(\Omega\) is connected in series with a variable capacitor \( C_x \). The series circuit is excited by a 10 V sinusoidal voltage source of angular frequency 1000 rad/s. As the value of the capacitor is varied, a maximum voltage of 30 V was observed across it. Neglecting skin effect, the value of the inductance of the coil in millihenry is \(\underline{\hspace{2cm}}\).

Hint:

When maximum voltage across a capacitor occurs in an LC circuit, the inductive reactance equals the capacitive reactance.

Answer 1

Correct Answer: 30

The impedance of the series LC circuit is given by: \[ Z = R + j\left( \omega L - \frac{1}{\omega C} \right) \] where \( R = 10 \, \Omega \), \( \omega = 1000 \, \text{rad/s} \), and the maximum voltage across the capacitor is \( 30 \, \text{V} \). The maximum voltage occurs when the reactance of the inductor and capacitor are equal in magnitude, which means: \[ \omega L = \frac{1}{\omega C} \] Solving for \( L \) using the given values and solving for the inductance, we get: \[ L = 30 \, \text{mH} \] Thus, the value of the inductance is \( 30 \, \text{mH} \).