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A circuit consists of a resistor,an inductor and a capacitor connected in series. If the resistance of a resistor is \( 25 \Omega \) and the value of inductive reactance is equal to capacitive reactance, then the net impedance of the circuit will be :

1. \( 5 \Omega \)
2. 25\Omega
3. \( 125 \Omega \)
4. \( 625 \Omega \)

Correct answer: 25\Omega

Solution

In a series RLC circuit, the impedance is \(Z=\sqrt{R^2+(X_L-X_C)^2}\). Since \(X_L=X_C\), the reactive term becomes zero, so the impedance equals the resistance alone. Therefore the net impedance is \(25\,\Omega\).

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