NEET Alternating Currents — Set 6

Question 1

A transformer has $ N_p = 100 $ and $ N_s = 200 $. If the primary voltage is $ 220 \, \text{V} $ (rms), what is the secondary voltage?

Accepted Answer

$ \frac{V_s}{V_p} = \frac{N_s}{N_p} $. $ V_s = V_p \times \frac{N_s}{N_p} = 220 \times \frac{200}{100} = 440 \, \text{V} $.

Question 2

What is the average power dissipated in a purely capacitive circuit over one complete cycle?

Accepted Answer

Power: $ p_C = i v = i_m v_m \cos (\omega t) \sin (\omega t) = \frac{i_m v_m}{2} \sin (2\omega t) $. Average over a cycle: $ P_C = \frac{i_m v_m}{2} \langle \sin (2\omega t) \rangle = 0 $, since $ \langle \sin (2\omega t) \rangle = 0 $.

Question 3

A $ 18 \, \mu\text{F} $ capacitor is connected to a $ 110 \, \text{V} $, $ 60 \, \text{Hz} $ AC source. What is the rms current?

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 60 = 376.8 \, \text{rad/s} $. $ C = 18 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{376.8 \times 18 \times 10^{-6}} \approx 147.3 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{110}{147.3} \approx 0.747 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 6

Q1. A transformer has \( N_p = 100 \) and \( N_s = 200 \). If the primary voltage is \( 220 \, \text{V} \) (rms), what is the secondary voltage?

Q2. What is the average power dissipated in a purely capacitive circuit over one complete cycle?

Q3. A \( 18 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?

Q4. In an AC circuit with a series combination of resistor and capacitor, what happens to the phase difference if the frequency approaches infinity?

Q5. A \( 50 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the inductive reactance?

Q6. A \( 30 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the peak current?

Q7. A series LCR circuit has \( R = 100 \, \Omega \), \( X_L = 80 \, \Omega \), \( X_C = 60 \, \Omega \). What is the impedance?

Q8. What is the effect on the power factor of an LCR series circuit when the frequency is decreased below resonance?

Q9. A series LCR circuit with \( R = 25 \, \Omega \) is at resonance with a \( 200 \, \text{V} \) (rms) source. What is the rms current?

Q10. A \( 80 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?