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  • Can someone explain - Electromagnetic Induction and Alternating currents - JEE Main-3

In an a.c. circuit, the instantaneous e.m.f. and current are given by e=100 sin 30 t

i= 20 sin \left ( 30 t-\frac{\pi }{4} \right ).

 In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively :

  • Option 1)

    50,0

  • Option 2)

    50,10

  • Option 3)

    \frac{1000}{\sqrt{2}}, 10

  • Option 4)

    \frac{50}{\sqrt{2}}, 0

 

Answers (2)

As we learnt that

 

Average power (True power) -

P_{av}= V_{rms}\: \: i_{rms}\cos \phi

-

 

e= 100 sin 30t

i= 20 sin(3rt-\pi /4)

P_{av}=e_{rms}.i_{rms}.cos\phi =\frac{100}{\sqrt{2}}.\frac{20}{\sqrt{2}}.\frac{1}{\sqrt{2}}=\frac{1000}{\sqrt{2}}W

Wattless current= \frac{I_{0}}{\sqrt{2}}sin \phi =\frac{20}{\sqrt{2}}.\frac{1}{\sqrt{2}}=10 A

 

 


Option 1)

50,0

This is incorrect

Option 2)

50,10

This is incorrect

Option 3)

\frac{1000}{\sqrt{2}}, 10

This is correct

Option 4)

\frac{50}{\sqrt{2}}, 0

This is incorrect

Posted by

Vakul

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