AC Voltage and Current Peak and RMS Values - UNSOLVED PRACTICE SET
Chapter: Alternating Current | Topic: AC Voltage and Current Peak and RMS Values
AC VOLTAGE AND CURRENT PEAK AND RMS VALUES - UNSOLVED PRACTICE SET
Topic: AC Voltage and Current Peak and RMS Values
Multiple Choice Questions
Q1. The RMS value of an alternating current is equal to:
- The maximum value of the current
- The average value of the current over one complete cycle
- The steady current that produces the same heating effect in a given resistor
- Half of the peak value of the current
Q2. For a sinusoidal AC voltage given by V = Vโ sin ฯt, the average value over one complete cycle is:
- Vโ/โ2
- 2Vโ/ฯ
- Zero
- Vโ
Q3. The peak value of a 220 V AC supply (RMS) is approximately:
- 220 V
- 311 V
- 156 V
- 440 V
Q4. The form factor of a sinusoidal AC waveform is defined as the ratio of:
- Peak value to RMS value
- RMS value to average value
- Average value to RMS value
- Peak value to average value
Q5. A sinusoidal alternating current has a peak value of 5 A. Its RMS value is:
- 5 A
- 5/โ2 A
- 5โ2 A
- 10 A
Q6. The frequency of AC supply in India is 50 Hz. The time period of one complete cycle is:
- 50 s
- 0.02 s
- 0.05 s
- 20 s
Short Answer Questions
Q7. Define the RMS value of an alternating current. Why is RMS value more commonly used than the average value for AC measurements?
Q8. The instantaneous value of an AC voltage is given by V = 100 sin(100ฯt) volts. Find its peak value, RMS value, and frequency.
Q9. Why is the average value of a sinusoidal AC taken over one complete cycle zero? Over what interval should the average value be calculated to get a meaningful non-zero result?
Q10. A student measures the voltage of an AC source using a voltmeter and gets a reading of 230 V. Is this the peak value or the RMS value? Explain.
Q11. Write the relationship between peak value, average value, and RMS value for a sinusoidal alternating current.
Q12. Why do we use RMS values instead of peak values when specifying AC voltage ratings on electrical appliances like refrigerators and TVs?
Long Answer Questions
Q13. Derive the expression for the RMS value of a sinusoidal alternating current. Show that I_rms = Iโ/โ2, where Iโ is the peak value.
Q14. Explain why the average value of a sinusoidal AC over a complete cycle is zero, but the average value over half a cycle is non-zero. Derive the expression for the average value over half a cycle.
Q15. Distinguish between peak value, average value, and RMS value of an alternating current. Why is the RMS value considered the most practical measure for AC circuits?
Numerical & Application-Based Problems
Q16. An alternating voltage is represented by the equation V = 200 sin(314t) volts.
(a) Determine the peak voltage, RMS voltage, frequency, and time period.
(b) Calculate the instantaneous voltage at t = 5 ms.
(c) At what time(s) during the first cycle does the voltage reach 100 V?
Q17. An AC source delivers a current I = 10 sin(100ฯt) amperes through a resistor of 10 ฮฉ.
(a) Calculate the peak current, RMS current, and frequency of the AC.
(b) Find the peak voltage and RMS voltage across the resistor.
(c) Calculate the heat produced in the resistor in 10 minutes.
Q18. In your home, the electricity board supplies AC voltage with a frequency of 50 Hz. Your father buys a new electric heater rated at 1000 W, 230 V.
(a) Calculate the peak voltage of the AC supply.
(b) Determine the RMS current drawn by the heater when operating at its rated power.
(c) A voltmeter in your school lab shows a reading of 11.3 V for an unknown AC source. A student claims the peak voltage is 16 V. Verify this claim with calculation.
(d) Explain why the rating on your home appliances mentions 230 V and not the peak voltage.