# RL circuit DE

1. Aug 19, 2007

### ehrenfest

Can someone link me to a website that shows how to solve the DE

dI/dt + (R/L)I = V/L

where R is resistance, L is capacitance, I is current, V is voltage.

I understand how the solution works when you plug it in but I want to know the DE method that was used to get that solution.

2. Aug 19, 2007

### olgranpappy

Supposing that R and L (and why not V too) are independent of time, then just
multiply both sides by $$e^{t(R/L)}$$ and you can rewrite the LHS as
$$\frac{d}{dt}\left(Ie^{t(R/L)}\right)$$

and then integrate over time; the integral of the LHS is trivial and the integral of the RHS is just an exponential, then don't forget the constant term, etc and solve for I(t) with algebra.

3. Aug 19, 2007

### ehrenfest

Thanks. I remember that from diffy q class now. What is that method called so I do not forget it again?

4. Aug 19, 2007

### Mindscrape

Just use the general solution method. Find the homogeneous solution and the particular solution.

Olgran used an integrating factor.

Last edited: Aug 20, 2007
5. Aug 19, 2007