# RLC transient analysis

1. Nov 7, 2015

### Junior

Let's say we have a free-source series RLC circuit. The differential equation that describes the behavior of the transient is given by $$Ri+L\frac{di}{dt}+V=0$$, where V is the potential difference across the capacitor. But I have trouble understanding the way this equation is developed. For example, suppose that we have the following situation:

But if I apply the loop rule, I get:

$$-V+Ri+L\frac{di}{dt}=0$$

What is wrong here? In the book they apply the loop rule to the same circuit above, but with the polarity of the capacitor inverted. But doesn't the current leave the positive terminal of it?