NEET Alternating Currents — Set 14

Question 1

A series LCR circuit with $ R = 70 \, \Omega $, $ X_L = 90 \, \Omega $, $ X_C = 40 \, \Omega $ has a $ 210 \, \text{V} $ (rms) source. What is the power dissipated?

Accepted Answer

$ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{70^2 + (90 - 40)^2} = \sqrt{4900 + 2500} = \sqrt{7400} \approx 86 \, \Omega $. RMS current: $ I = \frac{V}{Z} = \frac{210}{86} \approx 2.442 \, \text{A} $. Power: $ P = I^2 R = (2.442)^2 \times 70 \approx 417.6 \, \text{W} $.

Question 2

A $ 80 \, \Omega $ resistor and $ 25 \, \mu\text{F} $ capacitor are in series with a $ 220 \, \text{V} $, $ 50 \, \text{Hz} $ source. What is the impedance?

Accepted Answer

$ X_C = \frac{1}{\omega C} = \frac{1}{314 \times 25 \times 10^{-6}} \approx 127.4 \, \Omega $. $ Z = \sqrt{R^2 + X_C^2} = \sqrt{80^2 + 127.4^2} = \sqrt{6400 + 16230.76} \approx 150.5 \, \Omega $.

Question 3

A light bulb rated at $ 100 \, \text{W} $ operates on a $ 220 \, \text{V} $ (rms) AC supply. What is the peak voltage across the bulb?

Accepted Answer

Peak voltage: $ v_m = \sqrt{2} V $. Given: $ V = 220 \, \text{V} $ (rms). $ v_m = 1.414 \times 220 = 311.08 \, \text{V} \approx 311 \, \text{V} $.

NEET Physics: Alternating Currents — Practice Set 14

Q1. A series LCR circuit with \( R = 70 \, \Omega \), \( X_L = 90 \, \Omega \), \( X_C = 40 \, \Omega \) has a \( 210 \, \text{V} \) (rms) source. What is the power dissipated?

Q2. A \( 80 \, \Omega \) resistor and \( 25 \, \mu\text{F} \) capacitor are in series with a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q3. A light bulb rated at \( 100 \, \text{W} \) operates on a \( 220 \, \text{V} \) (rms) AC supply. What is the peak voltage across the bulb?

Q4. A \( 45 \, \Omega \) resistor and \( 18 \, \mu\text{F} \) capacitor are in series with a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the impedance?

Q5. In an AC circuit with a resistor and capacitor in series, why can the sum of individual voltages exceed the source voltage?

Q6. A \( 25 \, \Omega \) resistor is connected to a \( 125 \, \text{V} \) (rms) AC source. What is the rms current?

Q7. A \( 212.1 \, \text{V} \) (peak) AC source is connected to a \( 75 \, \Omega \) resistor. What is the average power consumed?

Q8. A \( 141.4 \, \text{V} \) (peak) AC source is connected to a \( 50 \, \Omega \) resistor. What is the average power consumed?

Q9. In an AC circuit with a capacitor and resistor in series, how does the phase difference between voltage and current change if the capacitance is increased?

Q10. In an AC circuit with only a resistor, what is the value of the power factor?