NEET Alternating Currents — Set 15

Question 1

A $ 75 \, \text{mH} $ inductor is connected to a $ 110 \, \text{V} $, $ 60 \, \text{Hz} $ AC source. What is the rms current?

Accepted Answer

$ X_L = \omega L $, $ \omega = 2\pi \times 60 = 376.8 \, \text{rad/s} $. $ L = 75 \times 10^{-3} \, \text{H} $. $ X_L = 376.8 \times 0.075 = 28.26 \, \Omega $. RMS current: $ I = \frac{V}{X_L} = \frac{110}{28.26} \approx 3.89 \, \text{A} $.

Question 2

Why does the impedance of an AC circuit with only an inductor increase with frequency?

Accepted Answer

The impedance in a purely inductive circuit is the inductive reactance ($ X_L = \omega L $), where $ \omega = 2\pi f $. As frequency ($ f $) increases, $ \omega $ increases linearly, causing $ X_L $ (and thus impedance) to increase proportionally.

Question 3

A $ 200 \, \Omega $ resistor and $ 15 \, \mu\text{F} $ capacitor are in series with a $ 220 \, \text{V} $, $ 50 \, \text{Hz} $ source. What is the voltage across the capacitor?

Accepted Answer

$ X_C = \frac{1}{\omega C} = \frac{1}{314 \times 15 \times 10^{-6}} \approx 212.3 \, \Omega $. $ Z = \sqrt{200^2 + 212.3^2} \approx 291.5 \, \Omega $. RMS current: $ I = \frac{V}{Z} = \frac{220}{291.5} \approx 0.755 \, \text{A} $. Voltage across capacitor: $ V_C = I X_C = 0.755 \times 212.3 \approx 160.3 \, \text{V} $.

NEET Physics: Alternating Currents — Practice Set 15

Q1. A \( 75 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?

Q2. Why does the impedance of an AC circuit with only an inductor increase with frequency?

Q3. A \( 200 \, \Omega \) resistor and \( 15 \, \mu\text{F} \) capacitor are in series with a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the voltage across the capacitor?

Q4. What is the significance of the phase difference being 90° in a purely reactive AC circuit?

Q5. A \( 20 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the peak current?

Q6. A series LCR circuit has \( R = 25 \, \Omega \), \( X_L = 50 \, \Omega \), \( X_C = 70 \, \Omega \). What is the phase angle?

Q7. Why does a transformer not work with direct current (DC)?

Q8. A \( 20 \, \Omega \) resistor is connected to a \( 100 \, \text{V} \) (rms) AC source. What is the rms current?

Q9. A \( 110 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q10. An AC voltage \( v = 141.4 \sin (100\pi t) \) V is applied across a \( 50 \, \Omega \) resistor. What is the rms current through the resistor?