JEE Main & Advanced Physics Alternating Current / प्रत्यावर्ती धारा Power in ac Circuits

In dc circuits power is given by \[P=Vi\]. But in ac circuits, since there is some phase angle between voltage and current, therefore power is defined as the product of voltage and that component of the current which is in phase with the voltage.

Thus \[P=V\,i\,cos\varphi \]; where V and i are r.m.s. value of voltage and current.

(1) Instantaneous power : Suppose in a circuit \[V={{V}_{0}}\sin \omega \,t\] and \[i={{i}_{0}}\sin (\omega \,t+\varphi )\]then \[{{P}_{\text{instantaneous}}}=Vi\]\[={{V}_{0}}{{i}_{0}}\sin \omega \,t\sin (\omega \,t+\varphi )\]

(2) Average power (True power) : The average of instantaneous power in an ac circuit over a full cycle is called average power. It's unit is watt i.e.

\[{{P}_{av}}={{V}_{rms}}{{i}_{rms}}\cos \varphi =\frac{{{V}_{0}}}{\sqrt{2}}.\frac{{{i}_{0}}}{\sqrt{2}}\cos \varphi =\frac{1}{2}{{V}_{0}}{{i}_{0}}\cos \varphi \]\[=i_{rms}^{2}R=\frac{V_{rms}^{2}R}{{{Z}^{2}}}\]

(3) Apparent or virtual power : The product of apparent voltage and apparent current in an electric circuit is called apparent power. This is always positive \[{{P}_{app}}={{V}_{rms}}{{i}_{rms}}=\frac{{{V}_{0}}{{i}_{0}}}{2}\]