In an `AC` circuit, `V` and `I` are given by `V=100sin(100t)volts, I=100sin(100t+(pi)/3)mA`. The power dissipated in circuit is

Options

A. `10^(4)` watt
B. 10 watt
C. 2.5 watt
D. 5 watt

Answer

C

Explanation

`E_("rms") = (100)/(sqrt(2))` volt.
`l_("rms") = (100)/(sqrt(2)) mA = (100)/(sqrt(2)) xx 10^(-3) A`, `phi = (pi)/(3)`
`E_("rms") l_("rms") cos phi = (100)/(sqrt(2)) xx (100)/(sqrt(2)) xx 10^(-3) xx "cos" (pi)/(3)`
`= (100 xx 100)/(2) xx 10^(-3) xx (1)/(2) = 2.5` watt