NEET Alternating Currents — Set 2

Question 1

A $ 15 \, \mu\text{F} $ capacitor is connected to a $ 110 \, \text{V} $, $ 60 \, \text{Hz} $ source. What is the rms current?

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 60 = 376.8 \, \text{rad/s} $. $ C = 15 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{376.8 \times 15 \times 10^{-6}} \approx 177 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{110}{177} \approx 0.621 \, \text{A} $.

Question 2

What is the significance of the rms value in specifying AC quantities?

Accepted Answer

The rms (root mean square) value of an AC quantity (e.g., voltage or current) is the equivalent DC value that produces the same average power in a resistive load. It accounts for the time-varying nature of AC, making it a standard measure for power calculations.

Question 3

A series LCR circuit with $ R = 80 \, \Omega $, $ X_L = 100 \, \Omega $, $ X_C = 40 \, \Omega $ has a $ 240 \, \text{V} $ (rms) source. What is the power dissipated?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{80^2 + (100 - 40)^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \, \Omega $. RMS current: $ I = \frac{V}{Z} = \frac{240}{100} = 2.4 \, \text{A} $. Power: $ P = I^2 R = (2.4)^2 \times 80 = 5.76 \times 80 = 460.8 \, \text{W} $.

NEET Physics: Alternating Currents — Practice Set 2

Q1. A \( 15 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the rms current?

Q2. What is the significance of the rms value in specifying AC quantities?

Q3. A series LCR circuit with \( R = 80 \, \Omega \), \( X_L = 100 \, \Omega \), \( X_C = 40 \, \Omega \) has a \( 240 \, \text{V} \) (rms) source. What is the power dissipated?

Q4. A \( 200 \, \text{V} \) (rms) source supplies a \( 80 \, \Omega \) resistor. What is the peak current?

Q5. In an AC circuit with only a resistor, how does the current behave relative to the applied voltage?

Q6. A transformer has \( N_p = 300 \), \( N_s = 150 \). If \( V_s = 120 \, \text{V} \) (rms), what is the primary voltage?

Q7. A \( 70 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q8. A \( 226.3 \, \text{V} \) (peak) AC source is connected to a \( 80 \, \Omega \) resistor. What is the average power consumed?

Q9. What happens to the average power dissipated in an AC circuit with only a capacitor over one complete cycle?

Q10. A \( 45 \, \mu\text{F} \) capacitor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the peak current?