Im trying to solve a problem in a book which goes as follows:
A 100mH inductor is connected in paralel with a 2k ohm resistor. The current through the inductor is given by:
a) Whats the voltage across the inductor Vl(t) ?
b) Whats the voltage across the resistor Vr(t)?
c) Is Vl+Vr=0?
That is all the data that is given, it doesnt mention a voltage or current source, so I figured that an inductor in paralel with a resistor in such configuration would be this:
In which case they are actually in series with each other, thus the current of the inductor should be the same current through the resistor.
Now, I calculate the voltage across the inductor:
And the Voltage across the resistor using ohms law:
The problem is that according to Kirchhoff's law, Vl + Vr should be zero, and they are clearly not. However as time goes by, it is true that Vl + Vr will tend to zero due to the exponential function (time (t) approaching infinity).
What troubles me is that Kirchhoffs law is not valid for short values of time, like t=1, or t=2, etc...
What am I doing wrong? what is going on here?