A coil of inductance 0.50 H and resistance 100 W is connected to a 240 V, 50 Hz A.C. supply.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

Given: Inductance = 0.50 H

Resistance R = 100 Ω

Voltage V = 240 V

Frequency = 50 Hz

The diagram is:

(a) Peak voltage is given by the following formula:

V₀ = √2 V

V₀ = √2 × 240V

On calculating, we get

V₀ = 339.41 V

Angular frequency is given by the formula ω = 2πv

Substituting value of v in above formula

ω = 2 × π × 50(Hz) = 100 π rad/s.

The maximum current in the coil can be calculated as follows:

On calculating, we get

I₀ = 1.82 A

(b) The equation for voltage and current are as follows:

V = V₀ cos ωt

I = I₀ cos (ωt-Ф)

At time t = 0, V = V₀

At t = Ф/ ω, I = I₀

Therefore, the time lag between maximum current and maximum voltage is Ф/ ω. Phase angle is given by the following relation:

tan Ф = ωL/R

tan Ф = (2 π × 50(Hz) × 0.5(H))/100

On calculating, we get

tan Ф = 1.57

or Ф = 57.5⁰

in rad Ф = 57.5π/180 rad

ωt = 57.5π/180

or

On calculating, we get

t = 3.2 ms