A coil with inductive reactance `X_(L) =30Omega` and impedance `Z = 50 Omega` is connected to the mains with effective voltage value `V = 100 V` Find the phase difference between the current and voltage as well as the heat power generated in the coil .

Explanation

`Z = R^(2) +X_(L)^(2)`
`(50)^(2) = R^(2) + (30)^(2)`
`R =40Omega`
phase difference between current and voltage
`tan phi = (X_(L))/R = (30)/(40) = (3)/(4) implies phi = 37^(@)`
`P = V_(rms) i_(rms) cos phi`
`=V_(rms) V_(rms)/R (R)/(Z) =(V_(rms)^(2)R)/(Z^(2))`
`((100)^(2)xx40)/((50)^(2) ) 160W`
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