NEET Alternating Currents — Set 18

Question 1

A $ 50 \, \Omega $ resistor and $ 20 \, \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 20 \times 10^{-6}} \approx 159.2 \, \Omega $. $ Z = \sqrt{R^2 + X_C^2} = \sqrt{50^2 + 159.2^2} = \sqrt{2500 + 25344.64} \approx 166.6 \, \Omega $.

Question 2

What happens to the current in a purely capacitive AC circuit when the frequency of the source increases?

Accepted Answer

In a purely capacitive circuit, the capacitive reactance ($ X_C = \frac{1}{\omega C} $) decreases as the frequency ($ f $, where $ \omega = 2\pi f $) increases. Since current is inversely proportional to reactance ($ I = \frac{V}{X_C} $), the current increases.

Question 3

A $ 28 \, \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 = 28 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 28 \times 10^{-6}} \approx 113.6 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{220}{113.6} \approx 1.936 \, \text{A} $.

NEET Physics: Alternating Currents — Practice Set 18

Q1. A \( 50 \, \Omega \) resistor and \( 20 \, \mu\text{F} \) capacitor are in series with a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q2. What happens to the current in a purely capacitive AC circuit when the frequency of the source increases?

Q3. A \( 28 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the rms current?

Q4. A series LCR circuit with \( R = 40 \, \Omega \) is at resonance with a \( 200 \, \text{V} \) (rms) source. What is the rms current?

Q5. A transformer has \( N_p = 300 \), \( N_s = 150 \). If \( V_s = 115 \, \text{V} \) (rms), what is the primary voltage?

Q6. A series LCR circuit has \( R = 10 \, \Omega \), \( X_L = 20 \, \Omega \), \( X_C = 30 \, \Omega \). What is the phase angle?

Q7. A \( 16 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the capacitive reactance?

Q8. A \( 50 \, \text{mH} \) inductor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the peak current?

Q9. A \( 30 \, \text{mH} \) inductor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the rms current?

Q10. A \( 150 \, \text{V} \) (rms) AC source supplies a \( 75 \, \Omega \) resistor. What is the average power consumed?