A coil of 0.01 henry inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find the impedance of the circuit and time lag between max. alternating voltage and current.

Explanation

Given, resistance of coil, R = 1 `Omega`
inductance of coil, L = 0.01 H
rms value of voltage , `e_(rms)` = 200 V
frequency of source , F = 50 Hz
Reactance of inductor is
`X_(L) = omega L = 2 pi f L = 2 pi xx 50 xx 0.01 = 3.14 Omega`
Impedance of circuit is
Z = `sqrt(R^(2) + X_(L)^(2)) = sqrt(1^(2) + (3.14)^(2))` = 3.3 `Omega`
If `phi` is the phase angle between voltage and current, then
`tan phi = (omega L)/(R ) = (2 xx 3.14 xx 50 xx 0.01)/(1)`
`rArr " " tan phi = 3.14`
`rArr " " phi = tan^(-1) (3.14) = 72 `
= 72 ` xx (pi)/(180) ` radian
Time lag between maximum alternating voltage and current is
`Delta t = (phi)/(omega) = (72 pi)/(180 xx 2 pi xx 50 ) = (1)/(25)` s