A current of `4A` flows in a coil when connected to a `12V DC` source. If the same coil is connected to a `12V, 50 rad//s AC` source, a current of `2.4A` flows in the circuit. Determine the inductance of the coil. Also, find the power developed in the circuit if a`2500muF` capacitor is connected in series with the coil.

Explanation

In dc circuits, inductor offers zero resistance
`I = (V)/R implies 4=(12)/R =3`
` 3Omega`
`i_(rms) = (V)/(Z)`
`2.4 = (12)/(Z) implies Z =5Omega`
`Z^(2) =R^(2) + X_(L)^(2)`
`(5)^(2) = (3)^(2) + X_(L)^(2) implies X_(L) =4Omega`
`omegaL = 4 implies L = (4)/(omega) = (4)/(50) = 0.08H`
`X_(C) = (1)/(omegaC) = (1)/(50 xx 2500 xx 10^(-6)) = 8Omega`
`Z = sqrt(R^(2) + (X_(C) -X_(L)^(2))`
`= sqrt((3)^(2) + (8 -4)^(2) =5Omega`
`cos phi = (R)/(Z) = (3)/(5)`
`P = V_(rms) i_(rms) cos phi`
` = V_(rms) . (V_(rms))/(Z) cosphi`
` = (12)^(2)/(5) xx (3)/(5) = 17.28W`


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