Physics HL · Chapter 20: Electromagnetic Induction
20.6 RMS Power and Transformer Links
Use RMS values for practical AC power and connect alternating flux to transformer voltage scaling.
Estimated time: 28 minutes
Why RMS Values Are Used
Instantaneous AC voltage and current oscillate, so practical ratings use RMS (root-mean-square) values. RMS corresponds to the DC value that would deliver the same average heating effect in a resistor. This is why mains ratings are RMS numbers, not peak numbers.
These relations hold for pure sinusoidal waveforms.
Average power in a resistive AC load is P_avg = V_rms I_rms, while instantaneous power oscillates through the cycle. In sinusoidal resistive cases, average power is half the peak instantaneous power from the V0 and I0 product.
Transformer Principle from Induction
A transformer uses alternating current in the primary coil to create changing flux in a shared core. That changing flux links the secondary coil and induces emf there. No changing flux means no transformer action, which is why transformers require AC rather than steady DC in normal operation.
Step-up voltage implies step-down current in ideal power-conserving transfer.
In real transformers, copper losses, core losses, and leakage flux reduce efficiency below 100%, but turn-ratio logic remains the first prediction tool. Keep units and turn ordering consistent to avoid simple inversion mistakes.
Note
Transmission grids use high voltage and low current to reduce I^2R cable losses over long distances.
Simulation: AC Power and RMS Inspector
Use one generator waveform to compare peak values, RMS equivalents, instantaneous power, and cycle-averaged power.
V0
147.781 V
Vrms
104.497 V
v(t)
138.868 V
i(t)
4.629 A
Irms
3.483 A
p(t)
642.813 W
Pavg
363.985 W
Period
20.000 ms
Test Yourself
An ideal transformer has Np = 500, Ns = 100, and primary voltage 230 V. Enter secondary voltage magnitude.
Hint: Apply Vs/Vp = Ns/Np.