Question

The inductance of an inductor becomes equal to capacitance when:

• A. Impedance is purely real
• B. Impedance is purely imaginary
• C. The resonance condition is satisfied
• D. None of the above

Hint:

In resonance, the inductive and capacitive reactances cancel each other, leading to a purely real impedance in the circuit.

Answer 1

The Correct Option is A

Step 1: Condition for resonance in LCR circuit
In a series LCR circuit, resonance occurs when the inductive reactance and capacitive reactance become equal in magnitude. That is:
\(X_L = X_C\)

Since, \(X_L = \omega L\) and \(X_C = \frac{1}{\omega C}\), at resonance:
\(\omega L = \frac{1}{\omega C}\)

Step 2: Effect on impedance
At resonance, the inductive and capacitive reactances cancel each other, so the net reactance becomes zero. Therefore, the impedance becomes purely resistive:
\(Z = R\)

Step 3: Physical interpretation
Since the imaginary part of impedance is zero, the circuit behaves as a purely resistive circuit and current becomes maximum.

Final Conclusion:
Thus, resonance occurs when \(X_L = X_C\), making the impedance purely real.