Mean Power (Cambridge (CIE) A Level Physics): Revision Note

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:

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

• 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:

$I_0=\sqrt{2}{I}_{r.m.s}$

• The peak (maximum) power and the mean (average) power are given by:

$P_{mean}={\left(I_{r.m.s}\right)}^{2}R$

$P_{peak}={I_0}^{2}R$

• Peak power can be written in terms of r.m.s current as

$P_{peak}={\left(\sqrt{2}{I}_{r.m.s}\right)}^{2}R$

• Therefore, peak power is related to mean power by:

$2{\left(I_{r.m.s}\right)}^{2}R=2P_{mean}$

$P_{mean}=\frac{P_{peak}}{2}$

• Therefore, it can be concluded that:

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

Mean power on a graph

Mean power is exactly half the maximum power