The a.c. Power Waveform | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

The a.c. Power Waveform

A resistor warms during both halves of an a.c. cycle. Reversing the current does not reverse the energy transfer.

Squaring keeps resistor power positive

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In a resistor, power follows I². Squaring removes the sign: power never becomes negative and has two humps per current cycle. For a sine wave, mean power is half the peak power.

P=I^2R

Symbols

$P$ = instantaneous power (W)
$I$ = instantaneous current (A)
$R$ = resistance of the load (Ω)

P=\dfrac{V^2}{R}

Squaring removes the sign, so resistor power never falls below zero.
Each current cycle produces two power humps. Power frequency is twice current frequency.
Every smooth power hump touches zero when the current crosses zero.

Your turnwaveform check

A sinusoidal current has frequency 50 Hz in a resistor. State the frequency and minimum value of the resistor's power waveform.

Show worked answer

The power frequency is 100 Hz because there are two humps per current cycle. Its minimum value is zero.