NEET Alternating Currents — Set 23

Question 1

A series LCR circuit has $ L = 1.5 \, \text{H} $, $ C = 35 \, \mu\text{F} $. What is the resonant frequency in Hz?

Accepted Answer

Resonant angular frequency: $ \omega_0 = \frac{1}{\sqrt{L C}} $. $ L = 1.5 \, \text{H} $, $ C = 35 \times 10^{-6} \, \text{F} $. $ \omega_0 = \frac{1}{\sqrt{1.5 \times 35 \times 10^{-6}}} \approx 138.3 \, \text{rad/s} $. $ f_0 = \frac{\omega_0}{2\pi} = \frac{138.3}{6.28} \approx 22 \, \text{Hz} $.

Question 2

In an AC circuit containing only a resistor, what happens to the power dissipated if the frequency of the source is doubled?

Accepted Answer

In a purely resistive AC circuit, power dissipated is $ P = I^2 R $, where $ I = \frac{V}{R} $, and $ R $ is constant. Since resistance does not depend on frequency, and assuming the rms voltage remains constant, the power dissipated remains unchanged when frequency doubles.

Question 3

A $ 60 \, \mu\text{F} $ capacitor is connected to a $ 110 \, \text{V} $, $ 60 \, \text{Hz} $ AC supply. What is the peak current in the circuit?

Accepted Answer

Capacitive reactance: $ X_C = \frac{1}{\omega C} $, where $ \omega = 2\pi f $. $ f = 60 \, \text{Hz} $, $ C = 60 \times 10^{-6} \, \text{F} $. $ \omega = 2 \times 3.14 \times 60 = 376.8 \, \text{rad/s} $. $ X_C = \frac{1}{376.8 \times 60 \times 10^{-6}} = 44.24 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{110}{44.24} = 2.487 \, \text{A} $. Peak current: $ i_m = \sqrt{2} I = 1.414 \times 2.487 \approx 3.52 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 23

Q1. A series LCR circuit has \( L = 1.5 \, \text{H} \), \( C = 35 \, \mu\text{F} \). What is the resonant frequency in Hz?

Q2. In an AC circuit containing only a resistor, what happens to the power dissipated if the frequency of the source is doubled?

Q3. A \( 60 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC supply. What is the peak current in the circuit?

Q4. A \( 268.7 \, \text{V} \) (peak) AC source is connected to a \( 95 \, \Omega \) resistor. What is the average power consumed?

Q5. A \( 23 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the rms current?

Q6. A \( 200 \, \text{V} \) (rms) AC source is connected to a series LCR circuit with \( R = 20 \, \Omega \) at resonance. What is the power dissipated?

Q7. A \( 17 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?

Q8. A \( 70 \, \Omega \) resistor and \( 14 \, \mu\text{F} \) capacitor are in series with a \( 210 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q9. A \( 180 \, \text{V} \) (rms) AC source supplies a \( 90 \, \Omega \) resistor. What is the average power consumed?

Q10. A \( 165 \, \text{V} \) (rms) AC source supplies a \( 55 \, \Omega \) resistor. What is the average power consumed?