# Homework Help: Current using kirchhoff's loop rule

1. May 8, 2010

### 8614smith

1. The problem statement, all variables and given/known data
By applying kirchhoffs rules, show that the in the RL circuit is given by: $$I=\frac{\epsilon}{R}\left(1-e^{-\frac{Rt}{L}}\right)$$

2. Relevant equations

kirchhoff's second rule: $$\epsilon-IR-L\frac{dI}{dt}=0$$

3. The attempt at a solution
$$\epsilon=IR+L\frac{dI}{dt}$$
$${\epsilon}dt=IRdt+LdI$$
$$\frac{\epsilon}{I}dt-Rdt=L\frac{1}{I}dI$$
then i thought to integrate both sides, LHS w.r.t t and RHS w.r.t I, but doing this on paper doesnt get to the right answer, am i going wrong somewhere with the rearranging??

2. May 8, 2010

### vela

Staff Emeritus
You can't integrate it the way you have it written. You want to get all the I's on one side and all the t's on the other first, then you can integrate it.

You could also just plug the solution in and show it satisfies the differential equation instead of solving the equation.