NEET Alternating Currents — Set 12

Question 1

A series LCR circuit has $ R = 10 \, \Omega $, $ X_L = 15 \, \Omega $, $ X_C = 5 \, \Omega $. What is the power factor?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{10^2 + (15 - 5)^2} = \sqrt{100 + 100} = 14.14 \, \Omega $. Power factor: $ \cos \phi = \frac{R}{Z} = \frac{10}{14.14} \approx 0.707 $.

Question 2

Why does the voltage across the inductor in a series LCR circuit equal the voltage across the capacitor at resonance, despite their phase difference?

Accepted Answer

At resonance, $ X_L = X_C $, and since $ V_L = I X_L $ and $ V_C = I X_C $ with the same current $ I $, their magnitudes are equal. However, they are 180° out of phase, so their vector sum is zero, not their magnitudes.

Question 3

A $ 100 \, \text{mH} $ inductor is connected to a $ 220 \, \text{V} $, $ 50 \, \text{Hz} $ AC source. What is the inductive reactance?

Accepted Answer

$ X_L = \omega L $, $ \omega = 2\pi f $. $ f = 50 \, \text{Hz} $, $ L = 100 \times 10^{-3} \, \text{H} $. $ \omega = 2 \times 3.14 \times 50 = 314 \, \text{rad/s} $. $ X_L = 314 \times 0.1 = 31.4 \, \Omega $.

NEET Physics: Alternating Currents — Practice Set 12

Q1. A series LCR circuit has \( R = 10 \, \Omega \), \( X_L = 15 \, \Omega \), \( X_C = 5 \, \Omega \). What is the power factor?

Q2. Why does the voltage across the inductor in a series LCR circuit equal the voltage across the capacitor at resonance, despite their phase difference?

Q3. A \( 100 \, \text{mH} \) inductor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the inductive reactance?

Q4. In a purely inductive AC circuit, the current lags the voltage by what phase angle?

Q5. Why does the voltage across an inductor in a series LCR circuit potentially exceed the source voltage at resonance?

Q6. A series LCR circuit has \( R = 15 \, \Omega \), \( X_L = 25 \, \Omega \), \( X_C = 40 \, \Omega \). What is the phase angle?

Q7. In a series LCR circuit, why does resonance not occur if either the inductor or capacitor is absent?

Q8. A \( 35 \, \text{mH} \) inductor is connected to a \( 110 \, \text{V} \), \( 60 \, \text{Hz} \) AC source. What is the rms current?

Q9. A \( 198.1 \, \text{V} \) (peak) AC source is connected to a \( 70 \, \Omega \) resistor. What is the average power consumed?

Q10. A series LCR circuit with \( R = 90 \, \Omega \), \( X_L = 120 \, \Omega \), \( X_C = 60 \, \Omega \) has a \( 270 \, \text{V} \) (rms) source. What is the power dissipated?