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

The total impedance \( Z \) in a series LCR circuit is defined as:

\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]

In this formula:

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

When resonance occurs, \( X_L \) equals \( X_C \), resulting in:

\[ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2} = R \]

At resonance, the impedance reaches its minimum value. According to Ohm's law, this minimum impedance leads to maximum current:

\[ I = \frac{V}{Z} \]

Consequently, the current is maximized because the inductive and capacitive reactances effectively cancel each other out.