NEET Alternating Currents — Set 7

Question 1

In an AC circuit with a resistor and inductor in series, what happens to the power factor if the inductance is increased?

Accepted Answer

In an RL series circuit, power factor $ \cos \phi = \frac{R}{Z} $, where $ Z = \sqrt{R^2 + X_L^2} $ and $ X_L = \omega L $. Increasing inductance increases $ X_L $, which increases $ Z $, reducing $ \cos \phi $ (closer to 0), as the circuit becomes more inductive.

Question 2

A series LCR circuit has $ L = 4 \, \text{H} $, $ C = 10 \, \mu\text{F} $. What is the resonant angular frequency?

Accepted Answer

$ \omega_0 = \frac{1}{\sqrt{L C}} $. $ L = 4 \, \text{H} $, $ C = 10 \times 10^{-6} \, \text{F} $. $ \omega_0 = \frac{1}{\sqrt{4 \times 10 \times 10^{-6}}} = \frac{1}{\sqrt{4 \times 10^{-5}}} \approx 158.1 \, \text{rad/s} $.

Question 3

What is the key requirement for an AC circuit to exhibit resonance?

Accepted Answer

Resonance in an AC circuit requires both inductance and capacitance to be present (e.g., in an LCR circuit). This allows the inductive and capacitive reactances to balance at a specific frequency, a condition not possible with only one reactive component.

NEET Physics: Alternating Currents — Practice Set 7

Q1. In an AC circuit with a resistor and inductor in series, what happens to the power factor if the inductance is increased?

Q2. A series LCR circuit has \( L = 4 \, \text{H} \), \( C = 10 \, \mu\text{F} \). What is the resonant angular frequency?

Q3. What is the key requirement for an AC circuit to exhibit resonance?

Q4. What is the role of a capacitor in improving the power factor of an AC circuit with an inductive load?

Q5. A \( 90 \, \text{mH} \) inductor is connected to a \( 220 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?

Q6. A sinusoidal voltage of peak value \( 283 \, \text{V} \) is applied to a \( 5 \, \Omega \) resistor. What is the rms current?

Q7. A \( 55 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the peak current?

Q8. A \( 8 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the capacitive reactance?

Q9. What happens to the current in a purely inductive AC circuit when the frequency of the source decreases?

Q10. A \( 15 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the capacitive reactance?