In an a.c. circuit, a resistor, a capacitor and an inductor are connected in series, in which $X_C = X_L= R$. The impedance of this circuit will be

$R$

The correct answer is Option (3) → $R$

Given: Series RLC circuit with $R = X_C = X_L$

Impedance of series RLC circuit: $Z = \sqrt{R^2 + (X_L - X_C)^2}$

Substitute $X_L = X_C = R$:

$Z = \sqrt{R^2 + (R - R)^2} = \sqrt{R^2 + 0} = R$

Impedance of the circuit: $Z = R$