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.

Answer

A, B, C, D

Explanation

`omega=2pif=(100pi)rad//s`
From the above two fingers, we can write
`V=400sin(omegat+theta_1)=400[100pit+pi/4]`
`i=20sin(omegat=theta_2)=20sin[100pit+pi/6]`
(b) Phase difference between `V` and `i`
`phi=(pi/4-pi/6)pi/12` or `15^@`
`P=V_("rms")i_("rms")cosphi=(400/sqrt2)(20/sqrt2)cos15^@`
`=3864W`