RMS and peak values of AC: Class 12 practice
For sinusoidal AC, I_rms = I₀/√2 and V_rms = V₀/√2. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Square roots
The idea behind rms and peak values of ac
For sinusoidal AC, I_rms = I₀/√2 and V_rms = V₀/√2. Mains '220 V' is the rms value; its peak is about 311 V. Average power in a resistor is V_rms I_rms.
Step-by-step method
- Peak = rms × √2; rms = peak ÷ √2.
- Power in a resistor = V_rms²/R.
- Read ω and f from v = V₀ sin ωt (f = ω/2π).
Worked example 1 (Basic)
An AC voltage has peak value 271 V. Find its rms value.
- V_rms = 271/√2
- = 191.63 V
- Answer: 191.63 V
Worked example 2 (Standard)
v = 217 sin(628t). Find the frequency and rms voltage.
- f = ω/2π = 99.95 Hz
- V_rms = 153.44 V
- Answer: 99.95 Hz, 153.44 V
Worked example 3 (Challenge)
v = 223 sin ωt is applied to a 88 Ω resistor. Find the average power.
- V_rms = 157.68 V
- P = V_rms²/R = 282.55 W
- Answer: 282.55 W
Common mistakes and misconceptions
- Using peak values in power formulas
- Confusing ω with f
Practice questions
- (Basic) An AC voltage has peak value 234 V. Find its rms value.
- (Basic) An AC voltage has peak value 246 V. Find its rms value.
- (Standard) v = 179 sin(314t). Find the frequency and rms voltage.
- (Standard) v = 320 sin(314.16t). Find the frequency and rms voltage.
- (Challenge) v = 66 sin ωt is applied to a 54 Ω resistor. Find the average power.
- (Challenge) v = 400 sin ωt is applied to a 15 Ω resistor. Find the average power.
Answer key with full working
- Q1: V_rms = 234/√2 → = 165.46 V → Answer: 165.46 V
- Q2: V_rms = 246/√2 → = 173.95 V → Answer: 173.95 V
- Q3: f = ω/2π = 49.97 Hz → V_rms = 126.57 V → Answer: 49.97 Hz, 126.57 V
- Q4: f = ω/2π = 50 Hz → V_rms = 226.27 V → Answer: 50 Hz, 226.27 V
- Q5: V_rms = 46.67 V → P = V_rms²/R = 40.33 W → Answer: 40.33 W
- Q6: V_rms = 282.84 V → P = V_rms²/R = 5333.33 W → Answer: 5333.33 W
Syllabus note
This skill is listed under "Alternating Current" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is rms and peak values of ac in?
"Alternating Current", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.