NEET Alternating Currents — Set 21

Question 1

A series LCR circuit has $ R = 20 \, \Omega $, $ X_L = 40 \, \Omega $, $ X_C = 60 \, \Omega $. What is the phase angle?

Accepted Answer

$ \tan \phi = \frac{X_C - X_L}{R} = \frac{60 - 40}{20} = 1 $. $ \phi = \tan^{-1}(1) = 45^\circ $. Since $ X_C > X_L $, the circuit is capacitive, and current leads voltage.

Question 2

A $ 60 \, \Omega $ resistor and $ 15 \, \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 15 \times 10^{-6}} \approx 212.3 \, \Omega $. $ Z = \sqrt{R^2 + X_C^2} = \sqrt{60^2 + 212.3^2} = \sqrt{3600 + 45071.29} \approx 220.8 \, \Omega $.

Question 3

What is the significance of the power factor being zero in an AC circuit?

Accepted Answer

A power factor of zero ($ \cos \phi = 0 $) means the phase difference between voltage and current is 90°, as in purely inductive or capacitive circuits. This indicates no average power is dissipated, as energy is only stored and released, not consumed.

NEET Physics: Alternating Currents — Practice Set 21

Q1. A series LCR circuit has \( R = 20 \, \Omega \), \( X_L = 40 \, \Omega \), \( X_C = 60 \, \Omega \). What is the phase angle?

Q2. A \( 60 \, \Omega \) resistor and \( 15 \, \mu\text{F} \) capacitor are in series with a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q3. What is the significance of the power factor being zero in an AC circuit?

Q4. A series LCR circuit with \( R = 100 \, \Omega \), \( L = 1 \, \text{H} \), \( C = 1 \, \mu\text{F} \) is at resonance. What is the impedance?

Q5. A series LCR circuit has \( L = 2.5 \, \text{H} \), \( C = 40 \, \mu\text{F} \). What is the resonant angular frequency?

Q6. In an AC circuit with a series LCR combination, why does the power dissipated depend only on the resistive component?

Q7. A series LCR circuit has \( R = 200 \, \Omega \), \( C = 15 \, \mu\text{F} \), and is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the impedance?

Q8. A \( 13 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the capacitive reactance?

Q9. A \( 200 \, \text{V} \) (rms) source supplies a \( 100 \, \Omega \) resistor. What is the peak current?

Q10. A transformer has \( N_p = 600 \), \( N_s = 300 \). If \( V_p = 240 \, \text{V} \) (rms), what is the secondary voltage?