[Physics Numerical] LR Series Circuit

A coil of inductance 0.50 H and resistance 100 Ω 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?

Given,
Inductance, L = 0.50 H
Resistance, R = 100 Ω
Effective voltage, E_v = 240 V
Frequency of the ac supply, f = 50 Hz

We can calculate,
Angular frequency, ω = 2πf = 100 π
Peak voltage, 

(a) The maximum amount of current in the coil is given by,

(b) In the LR circuit,

If, 
Now, At 
At 
∴ The time lag between voltage maximum and current maximum
Using the below-given relation, we can find the value of ϕ.
Therefore,

Thus, 

is the required time lag between the maximum voltage and maximum current.