Question

For a series LCR circuit, I vs ω curve is shown :

(a) To the left of ω_r, the circuit is mainly capacitive.

(b) To the left of ω_r, the circuit is mainly inductive.

(c) At ω_r, impedance of the circuit is equal to the resistance of the circuit.

(d) At ω_r, impedance of the circuit is 0.

Choose the most appropriate answer from the options given below.

• (a) and (d) only
• (b) and (d) only
• (a) and (c) only
• (b) and (c) only

Answer 1

The Correct Option is C

The question involves understanding the behavior of a series LCR circuit's impedance across different frequencies. The I vs. ω curve provided illustrates how current varies with angular frequency ω. Let's analyze the options given: 

1. To the left of ω_r (resonant frequency), the circuit is mainly capacitive:

In a series LCR circuit, if the frequency is less than the resonant frequency (ω < ω_r), the reactance of the capacitor dominates. Here, the circuit behaves like a capacitive circuit as the capacitive reactance (X_C = \(\frac{1}{\omega C}\)) is higher compared to the inductive reactance (X_L = ωL). This explains option (a) as correct.

1. To the left of ω_r, the circuit is mainly inductive:

This statement is incorrect because, as explained above, for frequencies below resonance, capacitive reactance dominates, not inductive.

1. At ω_r, the impedance of the circuit is equal to the resistance of the circuit:

At the resonant frequency ω_r, the inductive and capacitive reactances cancel each other out (X_L = X_C). Thus, the only impedance remaining in the circuit is due to the resistance (R), making option (c) correct.

1. At ω_r, the impedance of the circuit is 0:

This statement is incorrect because the impedance cannot be zero; it equals the resistance of the circuit at resonance.

Therefore, the most appropriate answer is: (a) and (c) only.