NEET Alternating Currents — Set 20

Question 1

A series LCR circuit with $ R = 50 \, \Omega $, $ X_L = 70 \, \Omega $, $ X_C = 30 \, \Omega $ has a $ 200 \, \text{V} $ (rms) source. What is the power dissipated?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{50^2 + (70 - 30)^2} = \sqrt{2500 + 1600} = \sqrt{4100} \approx 64 \, \Omega $. RMS current: $ I = \frac{V}{Z} = \frac{200}{64} \approx 3.125 \, \text{A} $. Power: $ P = I^2 R = (3.125)^2 \times 50 \approx 488.28 \, \text{W} $.

Question 2

In an LCR series circuit, if the frequency is below the resonant frequency, which component dominates the circuit's behavior?

Accepted Answer

Below resonance, $ \omega $ is low, making $ X_C = \frac{1}{\omega C} $ larger than $ X_L = \omega L $. Thus, the capacitive reactance dominates, and the circuit behaves as predominantly capacitive, with current leading voltage.

Question 3

A $ 240 \, \text{V} $ (rms) source supplies a $ 120 \, \Omega $ resistor. What is the peak current?

Accepted Answer

RMS current: $ I = \frac{V}{R} = \frac{240}{120} = 2 \, \text{A} $. Peak current: $ i_m = \sqrt{2} I = 1.414 \times 2 \approx 2.828 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 20

Q1. A series LCR circuit with \( R = 50 \, \Omega \), \( X_L = 70 \, \Omega \), \( X_C = 30 \, \Omega \) has a \( 200 \, \text{V} \) (rms) source. What is the power dissipated?

Q2. In an LCR series circuit, if the frequency is below the resonant frequency, which component dominates the circuit's behavior?

Q3. A \( 240 \, \text{V} \) (rms) source supplies a \( 120 \, \Omega \) resistor. What is the peak current?

Q4. A series LCR circuit has \( L = 6 \, \text{H} \), \( C = 10 \, \mu\text{F} \). What is the resonant angular frequency?

Q5. A \( 50 \, \Omega \) resistor and \( 20 \, \mu\text{F} \) capacitor are in series with a \( 110 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the voltage across the resistor?

Q6. A series LCR circuit with \( R = 50 \, \Omega \) is at resonance with a \( 250 \, \text{V} \) (rms) source. What is the rms current?

Q7. A \( 169.7 \, \text{V} \) (peak) AC source is connected to a \( 60 \, \Omega \) resistor. What is the average power consumed?

Q8. A \( 15 \, \Omega \) resistor is connected to a \( 75 \, \text{V} \) (rms) AC source. What is the rms current?

Q9. A series LCR circuit has \( R = 80 \, \Omega \), \( X_L = 60 \, \Omega \), \( X_C = 40 \, \Omega \). What is the impedance?

Q10. Why does an ideal transformer maintain constant power across its primary and secondary coils?