PHYSICS WORLD: Power

Sunday, 21 September 2014

Power

Main article: AC power

The relationship between voltage and the power delivered is

p(t) = \frac{v^2(t)}{R}

where

R

represents a load resistance.

Rather than using instantaneous power,

p(t)

, it is more practical to use a time averaged power (where the averaging is performed over any integer number of cycles). Therefore, AC voltage is often expressed as a root mean square (RMS) value, written as

V_{\rm rms}

, because

P_{\rm time~averaged} = \frac{{V^2}_{\rm rms}}{R}.

Power oscillation: $v(t)=V_\mathrm{peak}\sin(\omega t)$; $i(t)=\frac{v(t)}{R}=\frac{V_\mathrm{peak}}{R}\sin(\omega t)$; $P(t)=v(t)\ i(t)=\frac{(V_\mathrm{peak})^2}{R} \sin^2(\omega t)$