21.1.3 Mean Power

Mean Power

In mains electricity, current and voltage are varying all the time
This also means the power varies constantly, recall the equations for power:

$P = I V = I^{2} R = \frac{V^{2}}{R}$

Where:
- I = direct current (A)
- V = direct voltage (V)
- R = resistance (Ω)
The r.m.s values means equations used for direct current and voltage can now be applied to alternating current and voltage
These are also used to determine an average current or voltage for alternating supplies
Recall the equation for peak current:

$I_{0} = \sqrt{2} I_{r . m . s}$

$P_{m e a n} = {(I_{r . m . s})}^{2} R$

$P_{p e a k} = {I_{0}}^{2} R$

$P_{p e a k} = {(\sqrt{2} I_{r . m . s})}^{2} R$

$2 {(I_{r . m . s})}^{2} R = 2 P_{m e a n}$

$P_{m e a n} = \frac{P_{p e a k}}{2}$

The mean power in a resistive load is half the maximum power for a sinusoidal alternating current or voltage

Average power graph, downloadable AS & A Level Physics revision notes

Mean power is exactly half the maximum power

An alternating voltage supplied across a resistor of 40 Ω has a peak voltage V₀ of 240 V.Calculate the mean power of this supply.

Step 1: Write down the known quantities

Resistance, R = 40 Ω

Peak voltage, V₀ = 240 V

Step 2: Write out the equation for the peak power and calculate

Mean Power Worked Example equation 1

Mean Power Worked Example equation 2

Step 3: Calculate the mean power

Mean power = 1440 / 2 = 720 W