NEET Alternating Currents — Set 13

Question 1

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

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 50 = 314 \, \text{rad/s} $. $ C = 50 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 50 \times 10^{-6}} \approx 63.7 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{220}{63.7} \approx 3.45 \, \text{A} $. Peak current: $ i_m = \sqrt{2} I = 1.414 \times 3.45 \approx 4.88 \, \text{A} $.

Question 2

In an AC circuit with only a capacitor, what is the nature of the current when the voltage is at its peak?

Accepted Answer

In a purely capacitive circuit, the current leads the voltage by 90°. When the voltage is at its peak (maximum positive or negative), the current is zero because it reaches its peak 90° earlier and crosses zero at the voltage peak.

Question 3

Why does a purely capacitive AC circuit not dissipate power despite having current flow?

Accepted Answer

In a purely capacitive circuit, the current leads the voltage by 90°. The instantaneous power oscillates, but the average power over a cycle is zero because the energy is stored during one half-cycle and returned during the other, with no net dissipation.

NEET Physics: Alternating Currents — Practice Set 13

Q1. A \( 50 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the peak current?

Q2. In an AC circuit with only a capacitor, what is the nature of the current when the voltage is at its peak?

Q3. Why does a purely capacitive AC circuit not dissipate power despite having current flow?

Q4. A \( 180 \, \text{V} \) (rms) source supplies a \( 90 \, \Omega \) resistor. What is the peak current?

Q5. A series LCR circuit with \( R = 50 \, \Omega \) is at resonance with a \( 230 \, \text{V} \) (rms) source. What is the rms current?

Q6. A series LCR circuit has \( L = 5 \, \text{H} \), \( C = 20 \, \mu\text{F} \). What is the resonant angular frequency?

Q7. A \( 20 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the peak current?

Q8. A series LCR circuit has \( R = 50 \, \Omega \), \( X_L = 80 \, \Omega \), \( X_C = 60 \, \Omega \). What is the power factor?

Q9. A series LCR circuit has \( R = 20 \, \Omega \), \( X_L = 40 \, \Omega \), \( X_C = 60 \, \Omega \). What is the phase angle?

Q10. What is the role of resonance in the operation of a radio receiver?