NEET Alternating Currents — Set 11

Question 1

A series LCR circuit has $ R = 35 \, \Omega $, $ X_L = 55 \, \Omega $, $ X_C = 75 \, \Omega $. What is the phase angle?

Accepted Answer

$ \tan \phi = \frac{X_C - X_L}{R} = \frac{75 - 55}{35} = \frac{20}{35} \approx 0.571 $. $ \phi = \tan^{-1}(0.571) \approx 29.74^\circ $. Since $ X_C > X_L $, current leads voltage.

Question 2

A $ 20 \, \mu\text{F} $ capacitor is connected to a $ 220 \, \text{V} $, $ 50 \, \text{Hz} $ AC supply. What is the rms current?

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 50 = 314 \, \text{rad/s} $. $ C = 20 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 20 \times 10^{-6}} \approx 159.2 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{220}{159.2} \approx 1.38 \, \text{A} $.

Question 3

A $ 65 \, \text{mH} $ inductor is connected to a $ 230 \, \text{V} $, $ 50 \, \text{Hz} $ source. What is the peak current?

Accepted Answer

$ X_L = \omega L $, $ \omega = 2\pi \times 50 = 314 \, \text{rad/s} $. $ L = 65 \times 10^{-3} \, \text{H} $. $ X_L = 314 \times 0.065 = 20.41 \, \Omega $. RMS current: $ I = \frac{V}{X_L} = \frac{230}{20.41} \approx 11.27 \, \text{A} $. Peak current: $ i_m = \sqrt{2} I = 1.414 \times 11.27 \approx 15.94 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 11

Q1. A series LCR circuit has \( R = 35 \, \Omega \), \( X_L = 55 \, \Omega \), \( X_C = 75 \, \Omega \). What is the phase angle?

Q2. A \( 20 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC supply. What is the rms current?

Q3. A \( 65 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the peak current?

Q4. What is the condition for maximum power dissipation in a series LCR circuit?

Q5. A \( 19 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the rms current?

Q6. Why does the current amplitude in a series LCR circuit peak at the resonant frequency?

Q7. A \( 30 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the rms current?

Q8. A \( 210 \, \text{V} \) (rms) source supplies a \( 105 \, \Omega \) resistor. What is the peak current?

Q9. A series LCR circuit with \( R = 50 \, \Omega \), \( X_L = 30 \, \Omega \), \( X_C = 20 \, \Omega \) is connected to an AC source. What is the impedance?

Q10. A transformer has \( N_p = 350 \), \( N_s = 700 \). If \( V_s = 420 \, \text{V} \) (rms), what is the primary voltage?