NEET Alternating Currents — Set 10

Question 1

A series LCR circuit has $ L = 2 \, \text{H} $, $ C = 50 \, \mu\text{F} $. What is the resonant angular frequency?

Accepted Answer

Resonant frequency: $ \omega_0 = \frac{1}{\sqrt{L C}} $. $ L = 2 \, \text{H} $, $ C = 50 \times 10^{-6} \, \text{F} $. $ \omega_0 = \frac{1}{\sqrt{2 \times 50 \times 10^{-6}}} = \frac{1}{\sqrt{10^{-4}}} = 100 \, \text{rad/s} $.

Question 2

A $ 21 \, \mu\text{F} $ capacitor is connected to a $ 230 \, \text{V} $, $ 50 \, \text{Hz} $ AC source. What is the rms current?

Accepted Answer

$ X_C = \frac{1}{\omega C} $, $ \omega = 2\pi \times 50 = 314 \, \text{rad/s} $. $ C = 21 \times 10^{-6} \, \text{F} $. $ X_C = \frac{1}{314 \times 21 \times 10^{-6}} \approx 151.6 \, \Omega $. RMS current: $ I = \frac{V}{X_C} = \frac{230}{151.6} \approx 1.517 \, \text{A} $.

Question 3

A transformer has $ N_p = 450 $, $ N_s = 900 $. If $ V_p = 120 \, \text{V} $ (rms), what is the secondary voltage?

Accepted Answer

$ \frac{V_s}{V_p} = \frac{N_s}{N_p} $. $ V_s = V_p \times \frac{N_s}{N_p} = 120 \times \frac{900}{450} = 240 \, \text{V} $.

NEET Physics: Alternating Currents — Practice Set 10

Q1. A series LCR circuit has \( L = 2 \, \text{H} \), \( C = 50 \, \mu\text{F} \). What is the resonant angular frequency?

Q2. A \( 21 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the rms current?

Q3. A transformer has \( N_p = 450 \), \( N_s = 900 \). If \( V_p = 120 \, \text{V} \) (rms), what is the secondary voltage?

Q4. A \( 80 \, \Omega \) resistor is connected to a \( 160 \, \text{V} \) (rms) AC source. What is the rms current?

Q5. Why does an AC circuit with only an inductor exhibit a "wattless" current?

Q6. What is the primary reason AC voltage is preferred over DC voltage for long-distance power transmission?

Q7. A series LCR circuit has \( R = 130 \, \Omega \), \( X_L = 110 \, \Omega \), \( X_C = 90 \, \Omega \). What is the impedance?

Q8. A \( 100 \, \text{W} \) bulb is connected to a \( 110 \, \text{V} \) (rms) AC supply. What is the resistance of the bulb?

Q9. In a series LCR circuit at resonance, the power dissipated is \( 4800 \, \text{W} \) with \( R = 3 \, \Omega \). What is the rms current?

Q10. A \( 65 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?