Physics / A2 level
Use rms values to compare varying current with steady heating.
Alternating current reverses direction periodically. For a sinusoid through a fixed resistor, rms current gives the same average heating power as a direct current of that value. The signed mean over a full cycle is zero.
A diode can rectify a signal so current has one direction. A smoothing capacitor reduces ripple rather than making a perfect steady source. Transformers require changing magnetic flux and have losses in real operation.
A sinusoidal current can be written I = I₀ sin(ωt + φ). The peak I₀, angular frequency ω and phase φ describe different features. Period is 2π/ω. A graph crossing zero does not imply that the source has permanently stopped: current reverses through the next half-cycle. The signed mean over a complete symmetric cycle is zero, while the mean square current is positive.
For a sinusoid, Irms = I₀/√2 and Vrms = V₀/√2. In a constant resistor, average power is Irms²R, equal to the heating effect of a direct current of the same rms value. If peak current is 4 A through 5 Ω, mean power is (4²/2) × 5 = 40 W. The peak power is larger, so do not substitute peak values into an average-power formula.
A diode allows much greater conduction in one direction than the other. An ideal half-wave rectifier removes one half of an input cycle; a full-wave arrangement routes both halves into the same output-current direction. The result still varies with time. Full-wave rectification gives more frequent peaks, but it does not automatically produce a constant voltage. Real diodes also have forward-voltage drops and other non-ideal behaviour.
A capacitor across a load charges near suitable waveform peaks and discharges into the load between them, reducing ripple. Greater capacitance or a larger load resistance generally slows this discharge and reduces ripple in the simple model. More load current can increase the voltage fall between peaks. The remaining waveform is not a pure sinusoid, so the sinusoidal peak-to-rms conversion should not be applied automatically to every rectified or smoothed signal.
Positive and negative current cancel in a signed average, but resistive heating depends on current squared. Both directions contribute positive energy transfer to the resistor.
For a sinusoid; I₀ is peak current.
Average heating power in a fixed resistor.
Sinusoidal current with the chosen zero phase.
A sinusoidal current has peak 10 A. What is its rms value to three significant figures?
Irms = 10/√2 = 7.07 A.
Use a simulated sinusoidal source and resistor to compare peak readings with rms predictions.
Inspect simulated waveforms and resistive heating before considering rectification. Component availability differs between models; use circuit diagrams where a diode bridge is not provided, and never practise on mains supplies.
It predicts equivalent resistive heating.
Mean power depends on mean square current.
7.07 A
Irms = 10/√2 = 7.07 A.
Zero
Positive and negative half-cycles cancel in an arithmetic mean.