Question

In an L-C-R circuit, 100 volt alternating voltage is applied between end points. In the circuit, inductive reactance is \( X_L = 20 \, \Omega \), capacitive reactance is \( X_C = 20 \, \Omega \), and resistance is \( R = 5 \, \Omega \). The impedance of the circuit will be:

• A. 20 ohm
• B. 5 ohm
• C. 15 ohm
• D. 45 ohm

Hint:

In an L-C-R circuit, the reactance \( X_L - X_C \) can be simplified if the inductive and capacitive reactances are equal, leading to only the resistance determining the impedance.

Answer 1

The Correct Option is C

The impedance \( Z \) in an L-C-R circuit is calculated as: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] Given: - \( R = 5 \, \Omega \) - \( X_L = 20 \, \Omega \) - \( X_C = 20 \, \Omega \) Because \( X_L = X_C \), the reactance is 0: \[ Z = \sqrt{R^2} = \sqrt{5^2} = 5 \, \Omega \] Therefore, the answer is 5 ohms.