JEE Main On 08 April 2018 Question 27
Question: In an a.c. circuit, the instantaneous e.m.f. and current are given by $ \text{e=100 sin 30 t} $ $ \text{i=20 sin }( 30t-\frac{\pi }{4} ) $ . In one cycle of a.c., the average power consumed by the circuit and the wattles current are, respectively: [JEE Main Online 08-04-2018]
Options:
A) $ \frac{50}{\sqrt{2}},0 $
B) $ 50,0 $
C) $ 50,10 $
D) $ \frac{1000}{\sqrt{2}},10 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ e=100\sin (30t) $ $ i=20\sin ( 30t-\frac{\pi }{4} ) $
$ e _{rms}=\frac{100}{\sqrt{2}}volt, $
$ i _{rms}=\frac{20}{\sqrt{2}}amp $
Power factor $ =\cos \phi =cos( -\frac{\pi }{4} )=\frac{1}{\sqrt{2}} $
$ <P\gt=e _{rms}i _{rms}\cos \phi $
$ =\frac{100}{\sqrt{2}}\times \frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}} $
$ =\frac{1000}{\sqrt{2}}watt $ Wattles current $ =i _{rms}\sin \phi $
$ =\frac{20}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=10amp $
