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The maximum values of the alternating vo...

The maximum values of the alternating voltages and current are `400 V` and `20 A` respectively in a circuit connected to `50 Hz` supply and these quantities are sinusoidal. The instantaneous values of the voltage and current are `200sqrt2V` and `10 A`, respectively. At `t = 0`, both are increasing positively.
(a) Write down the expression for voltage and current at time `t`.
(b) Determine the power consumed in the circuit.

Text Solution

Verified by Experts

The correct Answer is:
`P=3864 W`
`omega=2pif=(100omega) "rad"//s`
From the above the two figures we can write :
`V=400 sin (omegat+theta_(1))=400 sin[100 pit+pi/4]`
`i=20 sin (omegat+theta_(2))=20 sin[100 pit+pi/6]`
Phase different between `V` and `i` :
`phi=(pi//4-pi//6)=pi/12` or `15^(@)`
`P=V_(rms)i_(rms)cosphi=(400/sqrt2)(20/sqrt2)cos 15^(@)=3864 W`
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