A coil of inductance `0.50H` and resistance `100 Omega` is connected to a `240V`, `50Hz` ac supply. What are the maximum current in the coil and the time lag between voltage maximum and current maximum?

Explanation

Here, `L = 0.5 H, R = 100 Omega, E_(v) = 200 V, v = 50 Hz`
`X_(L) = omega L = 2 pi v Lj = 2 pi xx 50 xx 0.5 = 50 pi`
`Z = sqrt(R^(2) + X_(L)^(2)) = sqrt(100^(2) + (50 pi)^(2)) = 186.1 Omega`
`I_(0) = (E_(0))/(Z) = (sqrt2 E_(v))/(Z) = (1.414 xx 200)/(186.1) = 1.5 A`
`tan phi = (omega L)/(R ) = (2 pi v L)/(R ) = (2 pi xx 50 xx 0.5)/(100) = 1.52 A`
`phi = tan^(-1) (1.57) = 57.5^(@) = (57.5 pi)/(180)` radian
`= 0.3194 pi`
Time lag, `t = (phi)/(omega) = (phi)/(2 pi v) = (0.3194 pi)/(2 pi xx 50)`
`= 3.194 xx 10^(3) s`