My professor wants us to derive a differential equation for the current in a circuit.
The circuit has a battery with voltage E, resistor with resistance (iR)??, and inductance L. It's in series.
The Attempt at a Solution
What REALLY confuses me are these things:
Why iR instead of R? Is the i supposed to represent current? Then why is it given for the resistance and not inductance? I don't think it could be a complex number.. it just wouldn't make sense.
Anyway, I assumed she meant R instead of iR. Then I set up a diff eq like this:
i(t)*R + L(d/dt)i(t) = 0
after a bit of math, I got
d(i(t))/i(t) = -(R/L)dt
and integrating some more math...
i(t) = Cexp(-(R/L)t) where C is some constant.
okay, that's fine. It seems to make sense to me
But then she wants us to solve it if i(0) = 0 and i(t=0) = 0.
First of all.. isn't she saying the exact same thing twice? i(0) = i(t=0) I'm guessing?
And second of all... according to my equation, i(0) = Cexp(0) = 0 implies C = 0, or that the whole expression is 0. How do I solve the differential equation if C = 0 exactly? Or does it only have a solution of 0?
Any clarification could help. Thanks!