Question

In an AC circuit, an inductor, a capacitor, and a resistor are connected in series with \( X_L = R = X_C \). The impedance of this circuit is:

• A. \( 2R^2 \)
• B. Zero
• C. \( R \)
• D. \( R\sqrt{2} \)

Hint:

When inductive and capacitive reactances are equal in a series circuit, the impedance is purely resistive.

Answer 1

The Correct Option is C

{Using Impedance Formula} 
\[ Z = \sqrt{(X_L - X_C)^2 + R^2} \] Since \( X_L = X_C \), \[ Z = \sqrt{(R - R)^2 + R^2} = \sqrt{0 + R^2} = R \] Thus, the correct answer is \( R \).