Question

The equation for an alternating current is given by i = 77 cos 314t. The

equation for corresponding voltage V = 200 sin 314t. What is the total

power consumed in the circuit.​

Answer 1

Given : The equation for an alternating current is given by i = 77 cos 314t.

The   equation for corresponding voltage V = 200 sin 314t.

To Find : total   power consumed in the circuit.​

Solution:

i = 77 cos 314t.

Im = 77 A

Irms = 77/√2

V = 200 sin 314t

 Vm = 200 V

Vrms = 200/√2 V

Power P = Vrms   Irms Cosθ

θ is the angle between Voltage and current

cos 314t and sin 314t has phase difference of 90°

  P = Vrms    Irms Cos 90°

Cos 90° = 0

=> P = (200/√2)(77/√2) . 0

=> P = 0

total   power consumed in the circuit ​ = 0

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