Solve this plzzz... ( just wanna know how to calculate time lag between current and the voltage )
Q. An inductor of 0.50 H and a resistance of 100 Ohm are connected in a series with an A.C. source $V_{rms}$ = 240 volt and 50 Hz. Find
(1) the maximum current in the inductor and
(2) the phase difference and the time lag between the current and the voltage.
(Ans. (1) 1.82 A (2) 57.5$°$ and 3.2 ms)
 

Dear Student
Inductance of the inductor, L = 0.50 H

Resistance of the resistor, R = 100 Ω

Potential of the supply voltage, V = 240 V

Frequency of the supply, ν = 50 Hz

(a) Peak voltage is given as:

Angular frequency of the supply,

ω = 2 πν

= 2π × 50 = 100 π rad/s

Maximum current in the circuit is given as:

(b) Equation for voltage is given as:

V = V 0 cos ω t

Equation for current is given as:

I = I 0 cos (ω t − Φ)

Where,

Φ = Phase difference between voltage and current

At time, t = 0.

V = V 0(voltage is maximum)

Forω t − Φ = 0 i.e., at time,

I = I 0 (current is maximum)

Hence, the time lag between maximum voltage and maximum current is.

Now, phase angle Φis given by the relation,

Hence, the time lag between maximum voltage and maximum current is 3.2 ms.
Regards