NEET Alternating Currents — Set 4

Question 1

A $ 9 \, \mu\text{F} $ capacitor is connected to a $ 230 \, \text{V} $, $ 50 \, \text{Hz} $ source. What is the capacitive reactance?

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 50 = 314 \, \text{rad/s} $. $ C = 9 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 9 \times 10^{-6}} \approx 353.7 \, \Omega $.

Question 2

A $ 60 \, \Omega $ resistor and $ 40 \, \mu\text{F} $ capacitor are in series with a $ 230 \, \text{V} $, $ 50 \, \text{Hz} $ source. What is the impedance?

Accepted Answer

$ X_C = \frac{1}{\omega C} = \frac{1}{314 \times 40 \times 10^{-6}} \approx 79.6 \, \Omega $. $ Z = \sqrt{R^2 + X_C^2} = \sqrt{60^2 + 79.6^2} = \sqrt{3600 + 6336.16} \approx 99.8 \, \Omega $.

Question 3

A series LCR circuit with $ R = 40 \, \Omega $, $ X_L = 50 \, \Omega $, $ X_C = 30 \, \Omega $ has a $ 120 \, \text{V} $ (rms) source. What is the power dissipated?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{40^2 + (50 - 30)^2} = \sqrt{1600 + 400} = \sqrt{2000} \approx 44.72 \, \Omega $. RMS current: $ I = \frac{V}{Z} = \frac{120}{44.72} \approx 2.68 \, \text{A} $. Power: $ P = I^2 R = (2.68)^2 \times 40 \approx 287.3 \, \text{W} $.

NEET Physics: Alternating Currents — Practice Set 4

Q1. A \( 9 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the capacitive reactance?

Q2. A \( 60 \, \Omega \) resistor and \( 40 \, \mu\text{F} \) capacitor are in series with a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q3. A series LCR circuit with \( R = 40 \, \Omega \), \( X_L = 50 \, \Omega \), \( X_C = 30 \, \Omega \) has a \( 120 \, \text{V} \) (rms) source. What is the power dissipated?

Q4. A transformer has \( N_p = 400 \), \( N_s = 800 \). If \( V_p = 120 \, \text{V} \) (rms), what is the secondary voltage?

Q5. A \( 14 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the rms current?

Q6. A \( 100 \, \Omega \) resistor and \( 50 \, \mu\text{F} \) capacitor are in series with a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q7. A \( 100 \, \Omega \) resistor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC supply. What is the average power consumed?

Q8. In a series LCR circuit, what happens to the total voltage across the inductor and capacitor at resonance?

Q9. In an AC circuit with only a capacitor, why does the current lead the voltage?

Q10. A transformer has \( N_p = 400 \), \( N_s = 800 \). If \( V_p = 120 \, \text{V} \) (rms), what is the secondary voltage?