| In an AC circuit the emf (e) and the current (i) at any instant are given respectively by [AIPMPT (S) 2008] |
| \[e={{E}_{0}}\sin \omega t\] |
| \[i={{I}_{0}}\sin (\omega t-\phi )\] |
| The average power in the circuit over one cycle of AC is |
A) \[\frac{{{E}_{0}}{{I}_{0}}}{2}\]
B) \[\frac{{{E}_{0}}{{I}_{0}}}{2}\sin \phi \]
C) \[\frac{{{E}_{0}}{{I}_{0}}}{2}\cos \phi \]
D) \[{{E}_{0}}{{I}_{0}}\]
Correct Answer: C
Solution :
| Key Idea: The power is defined as the rate at which work is being done in the circuit. |
| Power = rate of work done in one complete cycle. |
| or \[{{P}_{av}}=\frac{W}{T}\] |
| or \[{{P}_{av}}=\frac{({{E}_{0}}{{I}_{0}}\cos \phi )T/2}{T}\] |
| or \[{{P}_{av}}=\frac{{{E}_{0}}{{I}_{0}}\cos \phi }{2}\] |
| where \[\cos \phi \] is called the power factor of an AC circuit. |
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