NEET Alternating Currents — Set 8

Question 1

What is the physical significance of the term "wattless current" in an AC circuit?

Accepted Answer

"Wattless current" refers to the component of current in a purely reactive (inductive or capacitive) AC circuit that is 90° out of phase with the voltage. It does not contribute to average power dissipation, as power is zero when $ \cos 90° = 0 $, hence "wattless."

Question 2

A series LCR circuit has $ R = 40 \, \Omega $, $ X_L = 65 \, \Omega $, $ X_C = 25 \, \Omega $. What is the power factor?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{40^2 + (65 - 25)^2} = \sqrt{1600 + 1600} = \sqrt{3200} \approx 56.57 \, \Omega $. Power factor: $ \cos \phi = \frac{R}{Z} = \frac{40}{56.57} \approx 0.707 $.

Question 3

A $ 16 \, \mu\text{F} $ capacitor is connected to a $ 230 \, \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 = 16 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 16 \times 10^{-6}} \approx 199 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{230}{199} \approx 1.156 \, \text{A} $. Peak current: $ i_m = \sqrt{2} I = 1.414 \times 1.156 \approx 1.63 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 8

Q1. What is the physical significance of the term "wattless current" in an AC circuit?

Q2. A series LCR circuit has \( R = 40 \, \Omega \), \( X_L = 65 \, \Omega \), \( X_C = 25 \, \Omega \). What is the power factor?

Q3. A \( 16 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the peak current?

Q4. A \( 90 \, \text{mH} \) inductor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q5. A \( 95 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q6. A series LCR circuit has \( R = 90 \, \Omega \), \( X_L = 70 \, \Omega \), \( X_C = 50 \, \Omega \). What is the impedance?

Q7. A series LCR circuit has \( L = 8 \, \text{H} \), \( C = 5 \, \mu\text{F} \). What is the resonant angular frequency?

Q8. A \( 40 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the capacitive reactance?

Q9. A series LCR circuit has \( R = 30 \, \Omega \), \( X_L = 40 \, \Omega \), \( X_C = 60 \, \Omega \). What is the phase angle?

Q10. A series LCR circuit has \( R = 30 \, \Omega \), \( X_L = 50 \, \Omega \), \( X_C = 20 \, \Omega \). What is the power factor?