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Question:

In an a.c. circuit, the instantaneous e.m.f. and current are given by e=100sin30t, i=20sin(30t−π/4). In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively.

50√2,0

1000√2,10

50,0

50,10

Solution:

The correct option is D
1000√2,10
Pavg=VrmsIrmscosθ=(Vo/√2)(Io/√2)cosθ=(100/√2)(20/√2)cos45=1000√2watt
Wattless current =Irmsinθ=Io/√2sinθ=20/√2sin45=10amp