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
Answer & explanation
Correct answer: option 3
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: $Z = R$