Question

For a series RLC circuit \( R = X_L = 2X_C \). The impedance of the circuit and phase difference between \( V \) and \( I \) respectively will be:

• A. \( \sqrt{5} R, \tan^{-1}(2) \)
• B. \( \sqrt{5} X_C, \tan^{-1}(1/2) \)
• C. \( \sqrt{5} X_C, \tan^{-1}(1/2) \)
• D. \( \sqrt{5} R, \tan^{-1}(1/2) \)

Hint:

In series RLC circuits, the phase difference and impedance depend on the values of the resistance and reactances.

Answer 1

The Correct Option is D

In a series RLC circuit, the impedance \( Z \) is given by: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] Given that \( R = X_L = 2X_C \), we substitute the values and simplify to find the impedance and phase difference. The correct result is \( \sqrt{5} R \) and \( \tan^{-1}(1/2) \).
Final Answer: \[ \boxed{\sqrt{5} R, \tan^{-1}(1/2)} \]