Discussion Forum

1)

In an AC circuit, the instantaneous emf and current  are given by

  $e=100\sin30t$ , $i=20\sin\left(30t-\frac{\pi}{4}\right)$

In one cycle of AC , the average power consumed by the circuit and the wattless current are, respectively

Answer:

Option D

Explanation:

Given,$e=100\sin30t$ 

and $e=100\sin30t$ 

  Average power ,

   $P_{av}=V_{rms}I_{rms}\cos\phi=\frac{100}{\sqrt{2}}\times\frac{20}{\sqrt{2}}\times\cos\frac{\pi}{4}$

    = 1000/√2 watt

  Wattless current is,

$ I=I_{rms}\sin\phi=\frac{20}{\sqrt{2}}\times\sin\frac{\pi}{4}$

 = 20/2 = 10A

   P_av =1000/√2 watt and  I _wattless= 10A