Question

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

Answer 1

(a)

It is given that the inductance of the inductor, L=0⋅50H, the resistance of the

Resistor, R=100Ω, supply voltage, V=240V and the frequency of supply, ν=50Hz.

The formula of angular frequency is,

ω=2πν

Substitute the value of ν in the above equation.

ω=2π×50 =100π rad/s

The formula of maximum current in the circuit is,

I 0 = 2 V R 2 + ω 2 L 2

Substitute the values.

I 0 = 2 ×240 ( 100 ) 2 + ( 100π ) 2 ( 0⋅50 ) 2 I 0 =1⋅82A

Thus, the value of the maximum current in the circuit is 1⋅82A.

(b)

The equation of voltage is,

V= V 0 cos( ωt )

The equation of current is,

I= I 0 cos( ωt−ϕ )

The equation at t=0 is given as,

ωt−ϕ=0 t= ϕ ω (1)

The formula of phase angle is,

tanϕ= ωL R

Substitute the values.

tanϕ= 2π×50×0⋅5 100 =1⋅57 ϕ= 57⋅5π 180  rad

Substitute the value of ϕ in equation (1).

t= 57⋅5π 180×2π×50 t=3⋅19× 10 −3 s =3⋅19 ms

Thus, the time lag between maximum voltage and maximum current is 3⋅2 ms.