NEET Alternating Currents — Set 22

Question 1

A series LCR circuit has $ L = 4 \, \text{H} $, $ C = 25 \, \mu\text{F} $. What is the resonant angular frequency?

Accepted Answer

$ \omega_0 = \frac{1}{\sqrt{L C}} $. $ L = 4 \, \text{H} $, $ C = 25 \times 10^{-6} \, \text{F} $. $ \omega_0 = \frac{1}{\sqrt{4 \times 25 \times 10^{-6}}} = \frac{1}{\sqrt{10^{-4}}} = 100 \, \text{rad/s} $.

Question 2

A $ 24 \, \mu\text{F} $ capacitor is connected to a $ 230 \, \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 = 24 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 24 \times 10^{-6}} \approx 132.6 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{230}{132.6} \approx 1.734 \, \text{A} $.

Question 3

In an LCR circuit with $ R = 3 \, \Omega $, $ X_L = 8 \, \Omega $, $ X_C = 4 \, \Omega $, what is the power factor?

Accepted Answer

Impedance: $ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{3^2 + (8 - 4)^2} = \sqrt{9 + 16} = 5 \, \Omega $. Power factor: $ \cos \phi = \frac{R}{Z} = \frac{3}{5} = 0.6 $.

NEET Physics: Alternating Currents — Practice Set 22

Q1. A series LCR circuit has \( L = 4 \, \text{H} \), \( C = 25 \, \mu\text{F} \). What is the resonant angular frequency?

Q2. A \( 24 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the rms current?

Q3. In an LCR circuit with \( R = 3 \, \Omega \), \( X_L = 8 \, \Omega \), \( X_C = 4 \, \Omega \), what is the power factor?

Q4. In an AC circuit with a resistor and capacitor in series, what happens to the total voltage across the components compared to the source voltage?

Q5. A \( 60 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) source. What is the peak current?

Q6. A \( 220 \, \text{V} \) (rms), \( 50 \, \text{Hz} \) AC source is connected to a \( 44 \, \text{mH} \) inductor. Calculate the inductive reactance.

Q7. In an ideal AC circuit with only a capacitor, what is the relationship between the rates of change of voltage and current?

Q8. What happens to the current in an AC circuit containing only an inductor when the source frequency approaches zero?

Q9. A series LCR circuit has \( R = 60 \, \Omega \), \( X_L = 50 \, \Omega \), \( X_C = 30 \, \Omega \). What is the impedance?

Q10. A \( 26 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the rms current?