#### Electrical Systems

##### Power in AC Circuit

V and I are the rms values of voltage and current

$\mathrm{Dummy Text}$ $\mathrm{Dummy Text}$ $\mathrm{Dummy Text}°$

(-ve value of φ means current lags voltage)

Average Power is P

$\mathrm{P = VI cos\left(\phi \right)}$ $\mathrm{Dummy Text}$

$\mathrm{p is the instantaneous power}$

$\mathrm{Dummy Text}$

v is the sinusoidal voltage

i is the sinusoidal current due to voltage v

φ is the phase angle between v and i sinusoid

$v={V}_{m}\text{sin(ωt)}$

$i={I}_{m}\text{sin(ωt + φ)}$

The instantaneous power is given as

On simplification we get

The first term is constant for a given load and the second term is a sinusoid of frequency 2ω

In one cycle the net value of the second term is zero. The first term is the average power

P is the average power and V & I are rms values

The average power is also known as real power.