Question

In an LCR series circuit, at resonance,

• A. the impedance is maximum
• B. the current is minimum
• C. the current leads the voltage by \(\frac{π}{2}\)
• D. the current and voltage are in phase

Hint:

At resonance X_L = X_C so the impedance is minimum and equal to R.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
In a series LCR circuit, impedance is \(Z = \sqrt{R^2 + (X_L - X_C)^2}\). At resonance \(X_L = X_C\).

Step 2: Check each option
The reactive terms cancel, so \(Z = R\), the minimum value. So (A) is wrong.
The current \(I = V/R\) is maximum, not minimum, so (B) is wrong.
The phase angle is \(\tan\phi = \dfrac{X_L - X_C}{R} = 0\), so current and voltage are in phase. (C), saying current leads by \(\pi/2\), is wrong, and (D) is right.

Final Answer:
Current and voltage are in phase at resonance, option (D). \[ \boxed{\text{In phase}} \]