NEET Alternating Currents — Set 3

Question 1

A $ 160 \, \text{V} $ (rms) AC source supplies a $ 80 \, \Omega $ resistor. What is the average power consumed?

Accepted Answer

RMS current: $ I = \frac{V}{R} = \frac{160}{80} = 2 \, \text{A} $. Average power: $ P = I^2 R = 2^2 \times 80 = 320 \, \text{W} $.

Question 2

In an AC circuit with a series combination of resistor, inductor, and capacitor, what is the condition for the circuit to be purely resistive?

Accepted Answer

For an LCR series circuit to be purely resistive, the net reactance must be zero ($ X_L - X_C = 0 $), which occurs at resonance when $ X_L = X_C $. This makes the impedance equal to the resistance ($ Z = R $), and the circuit behaves as if only resistance is present.

Question 3

A series LCR circuit has $ R = 40 \, \Omega $, $ L = 5 \, \text{H} $, $ C = 80 \, \mu\text{F} $. What is the resonant frequency in Hz?

Accepted Answer

$ \omega_0 = \frac{1}{\sqrt{L C}} $. $ L = 5 \, \text{H} $, $ C = 80 \times 10^{-6} \, \text{F} $. $ \omega_0 = \frac{1}{\sqrt{5 \times 80 \times 10^{-6}}} = \frac{1}{\sqrt{4 \times 10^{-4}}} = 50 \, \text{rad/s} $. $ f_0 = \frac{50}{2 \times 3.14} \approx 7.96 \, \text{Hz} $.

NEET Physics: Alternating Currents — Practice Set 3

Q1. A \( 160 \, \text{V} \) (rms) AC source supplies a \( 80 \, \Omega \) resistor. What is the average power consumed?

Q2. In an AC circuit with a series combination of resistor, inductor, and capacitor, what is the condition for the circuit to be purely resistive?

Q3. A series LCR circuit has \( R = 40 \, \Omega \), \( L = 5 \, \text{H} \), \( C = 80 \, \mu\text{F} \). What is the resonant frequency in Hz?

Q4. A \( 55 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the rms current?

Q5. A \( 12 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the capacitive reactance?

Q6. In a purely capacitive AC circuit, the current leads the voltage by what phase angle?

Q7. A \( 120 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q8. A \( 150 \, \Omega \) resistor is connected to a \( 300 \, \text{V} \) (peak) AC supply. What is the rms current in the circuit?

Q9. In a step-up transformer, how does the current in the secondary coil compare to the primary coil, assuming ideal conditions?

Q10. A series LCR circuit has \( L = 3.5 \, \text{H} \), \( C = 8 \, \mu\text{F} \). What is the resonant angular frequency?