Question

In an RLC series circuit the value of \(R, L\) and \(C\) is given as \(R = 50\Omega\), \(L = 1.6\,H\) and \(C = 40\mu F\). Find the value inductive reactance \((X_L)\) at resonance.

• A. \(50\Omega\)
• B. \(100\Omega\)
• C. \(200\Omega\)
• D. \(400\Omega\)

Hint:

At resonance in RLC circuit: \[ X_L = X_C \] and \[ \omega = \frac{1}{\sqrt{LC}} \]

Answer 1

The Correct Option is C

Concept: At resonance in an RLC circuit, \[ X_L = X_C \] \[ \omega L = \frac{1}{\omega C} \] \[ \omega = \frac{1}{\sqrt{LC}} \] Inductive reactance \[ X_L = \omega L \]
Step 1: Find angular frequency at resonance. \[ \omega = \frac{1}{\sqrt{LC}} \] \[ \omega = \frac{1}{\sqrt{(1.6)(40\times10^{-6})}} \] \[ \omega = \frac{1}{\sqrt{64\times10^{-6}}} \] \[ \omega = \frac{1}{8\times10^{-3}} \] \[ \omega = 125 \]
Step 2: Calculate inductive reactance. \[ X_L = \omega L \] \[ X_L = 125 \times 1.6 \] \[ X_L = 200\Omega \] \[ \boxed{X_L = 200\Omega} \]