Simulation · Physics · Class 12
Why 220 V mains peaks at 311 V
From the lesson RMS values and average power in Alternating Current. Change the values and watch what happens.
Why 220 V mains peaks at 311 VPhysics · Class 12
The idea behind it
NCERT §7.2
- The power in the resistor at any instant is p = i²R = im²R sin²ωt. Since sin²ωt = ½(1 − cos 2ωt) and cos 2ωt averages to zero over a cycle, the average power is ½im²R.
- To write this like the dc formula P = I²R, define the root mean square (rms) or effective current I = im/√2 = 0.707 im. Then P = I²R.
- Likewise the rms voltage is V = vm/√2 = 0.707 vm, and V = IR, so P = V²/R = IV, exactly as for dc.
- The rms current is the steady current that would heat the same resistor at the same average rate.
- AC values are quoted as rms values unless stated otherwise. The household 220 V is an rms value; its peak is √2 × 220 = 311 V.
- Example 7.1: a bulb rated 100 W for 220 V has R = V²/P = 484 Ω; the source's peak voltage is 311 V; the rms current is P/V = 0.454 A.