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 = 0.50 H, R = 100 Omega, E_(v) = 240 V, v = 50 Hz, omega = 2 pi v = 100 pi, E_(0) sqrt2 E_(v) = sqrt2 xx 240 V`
(a) `I_(0) = (E_(0))/(sqrt(R^(2) + omega^(2) L^(2))) = (sqrt2 xx 240)/(sqrt(10^(4) + (100 pi xx 0.5)^(2))) = 1.82 A`
(b) In R -L circuit,
If `E = E_(0) cos omega t, I = I_(0) cos (omega t - phi)`
At `t = 0, E = E_(0)`, i.e., voltage is maximum.
At `t = (phi)/(omega). I = I_(0) cos (phi - phi) = I_(0) xx 1`, current is maximum
`:.` Time lag between voltage maximum and current maximum `= (phi)/(omega)`
As `tan phi = (omega L)/(R ) = (2 pi xx 50 xx 0.50)/(100) = (22)/(7 xx 2) = 1.571`
`phi = tan^(-1) (1.571) = 57.5^(@) = (57.5 pi)/(180)` radian
`:.` Time log `= (phi)/(omega) = (57.5 pi)/(180 xx 2 pi v) = (57.5)/(180 xx 2 xx 50) = 3.19 xx 10^(-5) `sec