Power in AC Circuit Power Factor - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: Power in AC Circuit Power Factor
POWER IN AC CIRCUIT POWER FACTOR - UNSOLVED PRACTICE SET
Topic: Power in AC Circuit Power Factor
Multiple Choice Questions
Q1. The power factor of an AC circuit is defined as:
- R/Z
- X_L/R
- X_C/R
- Z/R
Q2. In a purely resistive AC circuit, the power factor is:
- Zero
- 0.5
- 1
- Infinity
Q3. The average power in an AC circuit is given by:
- P = V_rms ร I_rms
- P = V_rms ร I_rms ร cos ฯ
- P = V_rms ร I_rms ร sin ฯ
- P = V_rmsยฒ / Z
Q4. In a purely inductive or purely capacitive circuit, the power factor is:
- 1
- 0.5
- Zero
- Infinity
Q5. The wattless current in an AC circuit is:
- The component of current in phase with voltage
- The component of current perpendicular to voltage
- The total current in the circuitn C
- The current at resonance
Q6. A low power factor in an AC circuit indicates:
- High efficiency
- Large wattless component of current
- Minimum current
- Resonance condition
Short Answer Questions
Q7. Define power factor. What is its value for a purely resistive, purely inductive, and purely capacitive circuit?
Q8. What is wattless current? In which type of AC circuit does it flow?
Q9. Why is it desirable to have a power factor close to unity in power transmission systems?
Q10. A series LCR circuit draws a current of 2 A from a 220 V, 50 Hz supply. The power consumed is 300 W. Calculate the power factor.
Q11. Distinguish between true power and apparent power in an AC circuit. Write their expressions.
Q12. How can the power factor of an inductive circuit be improved? Explain with a circuit diagram.
Long Answer Questions
Q13. Derive the expression for average power in an AC circuit. Show that P_avg = V_rms I_rms cos ฯ, where ฯ is the phase angle between voltage and current. Explain the significance of cos ฯ.
Q14. Explain what is meant by wattless current. Show that in a purely inductive or purely capacitive circuit, the average power consumed is zero, even though current flows through the circuit.
Q15. Discuss the importance of power factor in AC power transmission. Why do power companies charge industrial consumers for low power factor? How can power factor correction be achieved?
Numerical & Application-Based Problems
Q16. A series LCR circuit has R = 50 ฮฉ, L = 0.5 H, and C = 20 ฮผF. It is connected to a 200 V, 50 Hz AC supply.
(a) Calculate the impedance of the circuit.
(b) Find the current in the circuit.
(c) Determine the power factor.
(d) Calculate the true power and apparent power consumed by the circuit.
Q17. An inductive coil draws a current of 5 A when connected to a 220 V, 50 Hz AC supply. The power consumed is 550 W.
(a) Calculate the power factor of the coil.
(b) Find the resistance and inductance of the coil.
(c) What capacitor should be connected in series with the coil to make the power factor unity?
(d) Calculate the current drawn from the supply after power factor correction.
Q18. In a small factory in India, an induction motor draws 20 A from a 440 V, 50 Hz three-phase AC supply. The power factor is measured to be 0.6 lagging.
(a) Calculate the apparent power, true power, and reactive power consumed by the motor.
(b) The factory owner installs a capacitor bank to improve the power factor to 0.9 lagging. Calculate the new current drawn from the supply for the same true power.
(c) If the electricity board charges โน8 per kVA of apparent power, calculate the monthly savings (for 8 hours/day operation) due to power factor correction.
(d) Explain why industries in India are often penalized for low power factor and incentivized to improve it.