Question

Which one of the following curves represents the variation of impedance \( (Z) \) with frequency \( f \) in a series LCR circuit?

• A.
• B.
• C.
• D.

Hint:

For an LCR circuit:
- Impedance \( Z \) is minimum at resonance \( (\omega = \omega_0) \).
- \( Z \) increases as frequency deviates from \( \omega_0 \).
- \( X_L \) increases with frequency, while \( X_C \) decreases.

Answer 1

The Correct Option is C

Step 1: The impedance \( Z \) in a series LCR circuit is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \] where \( X_L = \omega L \) and \( X_C = \frac{1}{\omega C} \).
Step 2: At resonance frequency \( \omega_0 \), the inductive and capacitive reactances cancel:
\[ X_L = X_C \Rightarrow Z = R \]
Step 3: For frequencies below and above \( \omega_0 \), \( Z \) follows a characteristic curve, which is represented by option (C).