Question

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.

Answer 1

R = 1 Ω, L = 0.01 H, V = 200 V, v = 50 Hz.

Impedance of the circuit

`Z = sqrt(R^2 + X_L^2) = sqrt(R^2 + (2pivL)^2)`

= `sqrt((1)^2 + (2 xx 3.14 xx 50 xx 0.1)^2)`

= `sqrt(1 + 9.86) = sqrt(10.86)`

= 3.3 Ω

∴ For phase angle, tan `phi = Z/R`

`tan phi = X_L/R = (2pivL)/R = (2 xx 3.14 xx 50 xx 0.01)/1`

`tan phi` = 3.14

`phi` = tan^–1 3.14 = 72°

Phase difference

`phi = (72 xx pi)/180^circ` rad

`phi` = 1.20 radian

Time lag between alternating voltage and current

`phi` = ωt

`t = phi/ω = (72 xx pi)/(180 xx 2 xx pi xx 50) = 1/250` sec