JEE Main | 2018Current Electricity and Electrical InstrumentHard

Question

In an a. c. circuit, the instantaneous e.m.f. and current are given by

e = 100 sin 30 t 
i = 20 sin 30t-π4 

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

Options

A.

10002, 10

B.

502, 0​​​​​​​

C.

50, 0

D.

50, 10

Solution

Pavg = Vrms Irms cosθ
=V02I02cosθ
=1002202cos 45o
=10002 watt
wattless current = Irms sinθ
=I02 sin θ
=202 sin 45o
= 10 amp.

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