220 V of AC mains has a peak value near 311 V, and a sinusoidal current of peak I₀ reads I₀/√2 on an rms meter, so converting between peak and rms is the backbone of this Class 12 sheet. The key also records that in a pure capacitor current lags voltage by 90°.
Key Takeaways
An rms value of 220 V corresponds to a peak of about 311 V (Q1).
A sinusoidal current with peak value I₀ has rms value I₀/√2 (Q2).
In a capacitor the current lags the voltage by 90°.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The peak value of AC mains having an rms value of 220 V is approximately
(a) 155 V(b) 311 V(c) 440 V(d) 220 V
2.The rms value of a sinusoidal current with peak value I₀ is
(a) I₀/2(b) I₀/√2(c) √2 I₀(d) I₀
3.In a purely resistive AC circuit, the current and the voltage are
(a) In phase(b) Out of phase by 90°(c) Out of phase by 180°(d) Out of phase by 45°
4.In a purely inductive AC circuit, the current
(a) Leads the voltage by 90°(b) Lags the voltage by 90°(c) Is in phase with the voltage(d) Lags the voltage by 180°
5.The average value of a sinusoidal AC over a complete cycle is
(a) I₀(b) I₀/2(c) 0(d) I₀/√2
6.The reactance of an inductor of inductance L at angular frequency ω is
(a) ωL(b) 1/(ωL)(c) ωC(d) 1/(ωC)
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the relation between the rms value and the peak value of a sinusoidal AC.
8.Write the reactance of an inductor of inductance L at angular frequency ω.
9.Write the reactance of a capacitor of capacitance C at angular frequency ω.
10.In a purely capacitive AC circuit, how is the current related to the voltage?
11.What is the average value of a sinusoidal AC over a complete cycle?
12.Write the formula for the resonant frequency of an L-C-R series circuit.
13.Write the expression for the power factor in an AC circuit.
14.Define reactance.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The peak voltage of an AC supply is 311 V. Find its rms value.
16.An AC source has a peak current of 2 A. Find the rms value of the current.
17.Find the reactance of an inductor of inductance 0.5 H at an angular frequency of 200 rad/s.
18.Find the resonant frequency of an L-C circuit with L = 2 H and C = 8 µF.
19.The rms voltage of AC mains is 220 V. Find the peak voltage.
20.A circuit has a power factor of 0.5. What is the phase angle between the current and the voltage?
Answer Key
1. b) 311 V
2. b) I₀/√2
3. a) In phase
4. b) Lags the voltage by 90°
5. c) 0
6. a) ωL
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the peak value of 220 V AC mains?
About 311 V, option (b) in this worksheet (Q1).
What is the rms value of a sinusoidal current of peak I₀?
I₀/√2, option (b) in this worksheet (Q2).
In a capacitor, does current lead or lag voltage?
It lags the voltage by 90°.
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