A coil has a resistance of `10 Omega` and an inductance of `0.4` henry. It is connected to an AC source of `6.5 V, 30/(pi) Hz`. Find the average power consumed in the circuit.

Explanation

Given `R=10 W`,
`L=0.4 Henry`,
`E = 6.5 V`,
`f= 30/pi H_2`
`Z=sqrt(R^2 + X_L^2)`
`=sqrt (R^2 + ((2pi)//L)^2)`
Power `=V_(rms)I_(rms)cos theta`
`=6.5 xx 6.5/Z R/Z`
`=(6.5 xx 6.5 xx 10)/[sqrt(r^2) + (2 pi fL)^2]^2`
`=(6.5 xx 6.5 xx 10)/((10)^2 + ( 2pi.30//pi.04)^2)
`=(6.5 xx 6.5 xx 10)/(676)`
`=0.625 = 5/8 W`