Question

In a series LCR circuit connected to an AC source, at resonance, the current is maximum because:

• A. The inductive reactance is maximum
• B. The capacitive reactance cancels the inductive reactance
• C. The resistance is zero
• D. The reactances add up

Hint:

At resonance in a series LCR circuit, inductive and capacitive reactances cancel, minimizing impedance and maximizing current.

Answer 1

The Correct Option is B

In a series LCR circuit, the total impedance (\( Z \)) is given by: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] where: \begin{itemize} \( R \) is the resistance \( X_L = \omega L \) is the inductive reactance \( X_C = \frac{1}{\omega C} \) is the capacitive reactance \end{itemize} At resonance, \( X_L = X_C \), so: \[ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2} = R \] The impedance is minimized, leading to maximum current as per Ohm's law: \[ I = \frac{V}{Z} \] Hence, the current is maximum because inductive and capacitive reactances cancel each other.