Question

Resistance \( R \), inductance \( L \) and capacitor \( C \) are connected in series. The frequency of the alternating current source is \( n \) and resonant frequency is \( n_r \). Under which condition does the current lag behind the voltage?

• A. \( n = 0 \)
• B. \( n<n_r \)
• C. \( n = n_r \)
• D. \( n>n_r \)

Hint:

In an RLC circuit, when the driving frequency is less than the resonant frequency, the current lags behind the voltage.

Answer 1

The Correct Option is B

Step 1: Understanding the RLC Series Circuit.
In a series RLC circuit, the current lags behind the voltage under certain conditions, depending on the relationship between the driving frequency \( n \) and the resonant frequency \( n_r \). The resonant frequency is given by: \[ n_r = \frac{1}{2 \pi \sqrt{LC}} \] When the driving frequency is less than the resonant frequency, the circuit behaves inductively, and the current lags behind the voltage.
Step 2: Analysis of options.
- (A) \( n = 0 \): If the frequency is zero, there is no oscillation, and the current will not be defined as lagging.
- (B) \( n<n_r \): When the frequency is less than the resonant frequency, the inductive reactance dominates, and the current lags behind the voltage. This is the correct answer.
- (C) \( n = n_r \): At resonance, the current and voltage are in phase, meaning there is no lag.
- (D) \( n>n_r \): When the frequency is greater than the resonant frequency, the capacitive reactance dominates, and the current leads the voltage, not lags behind it.

Step 3: Conclusion.
The current lags behind the voltage when the frequency of the source is less than the resonant frequency, making option (B) the correct answer.