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
