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:

• \( R \) is the resistance
• \( X_L = \omega L \) is the inductive reactance
• \( X_C = \frac{1}{\omega C} \) is the capacitive reactance

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.