Calculating the current in an inductor.

Again, we recall that the voltage, V in an inductor is:

V = L di/dt So the current, i can be written as:

The voltage across a 10.6H inductor is given as: V = (3t + 25.4)^{1/2} volts. Find the current in the inductor at 5.25 seconds if the initial current is 6.15A.

Write the initial equation.

Now try the substitution for u, du and n.

u = 3t + 25.4 du = 3 dt n = 1/2

Now integrate:

i = 0.0314 2/3 u ^{3/2} + C

i = 0.0210 (3t + 25.4) ^{3/2} + C

We need some initial conditions in order to solve for C.

When t = 0, i = 6.15A

6.15 = 0.0210 (3(0) + 25.4) ^{3/2} + C

C = 3.46A

So: i = 0.0210 (3t + 25.4) ^{3/2} + 3.46

And when t = 5.25sec, i = 9.00A