NEET Alternating Currents — Set 5

Question 1

A series LCR circuit has $ R = 40 \, \Omega $, $ X_L = 60 \, \Omega $, $ X_C = 20 \, \Omega $. What is the power factor?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{40^2 + (60 - 20)^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 2

A $ 27 \, \mu\text{F} $ capacitor is connected to a $ 220 \, \text{V} $, $ 50 \, \text{Hz} $ source. What is the rms current?

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 50 = 314 \, \text{rad/s} $. $ C = 27 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 27 \times 10^{-6}} \approx 117.8 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{220}{117.8} \approx 1.867 \, \text{A} $.

Question 3

A $ 70 \, \text{mH} $ inductor is connected to a $ 230 \, \text{V} $, $ 60 \, \text{Hz} $ source. What is the peak current?

Accepted Answer

$ X_L = \omega L $, $ \omega = 2\pi \times 60 = 376.8 \, \text{rad/s} $. $ L = 70 \times 10^{-3} \, \text{H} $. $ X_L = 376.8 \times 0.07 = 26.38 \, \Omega $. RMS current: $ I = \frac{V}{X_L} = \frac{230}{26.38} \approx 8.72 \, \text{A} $. Peak current: $ i_m = \sqrt{2} I = 1.414 \times 8.72 \approx 12.33 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 5

Q1. A series LCR circuit has \( R = 40 \, \Omega \), \( X_L = 60 \, \Omega \), \( X_C = 20 \, \Omega \). What is the power factor?

Q2. A \( 27 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the rms current?

Q3. A \( 70 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the peak current?

Q4. A series LCR circuit has \( R = 20 \, \Omega \), \( X_L = 35 \, \Omega \), \( X_C = 55 \, \Omega \). What is the phase angle?

Q5. A \( 85 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q6. An AC source provides a peak voltage of \( 424.2 \, \text{V} \) to a \( 200 \, \Omega \) resistor. What is the average power consumed?

Q7. A \( 25 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?

Q8. A \( 10 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC supply. What is the peak current?

Q9. A transformer steps down \( 440 \, \text{V} \) to \( 220 \, \text{V} \). If the secondary current is \( 8 \, \text{A} \), what is the primary current?

Q10. A series LCR circuit has \( R = 110 \, \Omega \), \( X_L = 90 \, \Omega \), \( X_C = 70 \, \Omega \). What is the impedance?