A 30volt electromotive force is applied to an RLseries circu

A 30-volt electromotive force is applied to an RL-series circuit in which the inductance is 0.1 henry and the resistance is 50 ohms. Find the current I(t) if I(0) = 0. Determine the current as t .

Solution

We know that

L*di/dt + R*i = V(t)

and

i(0) = 0

L = 0.1 H

R = 50 ohm

V(t) = 30 V

0.1*di/dt + 50*i = 30

di/dt + 500*i = 300

using integrating factor method

IF = e^[integral (500*(t))]

IF = e^(500*t)

[e^(500*t)]\' = 300*e^(500*t)

e^(500*t)*i = 3*e^(500*t)/5 + c

i = 3/5 + c*e^(-500*t)

i(0) = 0

0 = 3/5 + c*e^0

c = -3/5

i = 0.6 - 0.6*e^(-500*t)

at t = infinite

i = 0.6 - 0.6*e^(-infinte)

i = 0.6 - 0.6*0

i = 0.6 Amp.