Two alternating voltages can have the same peak and produce different heating in the same resistor. The RMS voltage depends on the mean of the squared voltage over a cycle. Dividing the peak by √2 works for a sinusoidal waveform.
SEAB’s 2027 A-Level H2 Physics syllabus (9478) covers peak and RMS values, the sinusoidal formula and mean power in a resistive load. This original comparison uses an ideal square wave to show why the waveform matters.
- Identify the waveform and its peak magnitude.
- Find the RMS voltage for that waveform.
- Use RMS voltage squared divided by resistance to find mean power.
Worked example | A 12 V peak across a 6 Ω resistor
A sinusoidal voltage has a 12 V peak. Its RMS value is 12/√2 V. Across a 6 Ω resistor, the mean power is (12/√2)² ÷ 6 = 12 W. Its peak power is 12² ÷ 6 = 24 W.
An ideal square wave alternates between +12 V and −12 V for equal durations. The squared voltage is 144 V² in both halves. The mean squared voltage is therefore 144 V² and the RMS voltage is 12 V.
The square wave produces 144 ÷ 6 = 24 W of mean power. Its mean voltage is zero, just like the sine wave in this example. Squaring before averaging captures the heating during both positive and negative halves.
Why the peak power is the same
Both waveforms reach the same maximum voltage magnitude, so they have the same peak power across the same resistor. The sine wave spends part of the cycle at a lower magnitude. The ideal square wave stays at the peak magnitude apart from its instantaneous transitions.
The resistance is assumed constant. A real component whose resistance changes with temperature would need a model for that change before you use this comparison.
Match the mean powers
What peak should a sine wave have to produce the same mean power as the ±12 V square wave in the same resistor? It needs an RMS voltage of 12 V, so its peak must be 12√2 V, about 17.0 V.
Ask a study partner which quantity matches when the heating matches. The RMS voltage matches for the same resistance. The two peak voltages can differ.
Frequently asked questions
Does a zero mean voltage imply zero heating?
Use the mean of the squared voltage for an ideal resistor. Positive and negative voltages can both contribute to heating.
Is the sinusoidal RMS formula valid for a square wave?
Use the square wave’s own mean squared value. The factor 1/√2 belongs to a sine wave.
Official information
SEAB’s 2027 A-Level H2 Physics syllabus (9478), Topic 15 Current of Electricity. Checked 10 November 2026.