# Kirchoff's Loop Rule as applied to Capacitors?

1. Jan 19, 2008

### fatcat39

1. The problem statement, all variables and given/known data

How does the loop rule apply to capacitors? I can't find any examples of circuits containing capacitors and resistors where the loop rule is used. I know the loop rule measures potential differences, but I'm not quite sure if that has anything to do with capacitors? All the examples are 0 = V - IR - IR, etc.

2. Relevant equations

3. The attempt at a solution

2. Jan 19, 2008

### Tom Mattson

Staff Emeritus
Yes, the loop rule is used with capacitors all the time. The element law for a capacitor is $v=q/C$. In more advanced (calculus-based) courses this is written $i=C\frac{dv}{dt}$. Solving this for the voltage, one obtains:

$$v=\frac{1}{C}\int_{t_0}^ti(\tau)d\tau+v(t_0)$$

3. Jan 19, 2008

### esalihm

all the basics of RC circuits (RL and RLC circuits too) come from a basic application of Kirchoff's Loop principle.

4. Jan 20, 2008

### fatcat39

So when finding currents, the branch that a capacitor is on (in terms of current) is 0, right? since when a capacitor is full, no current flows.

5. Jan 20, 2008

### tim_lou

not necessarily. it depends on the situation. Since charging rate = current, current=0 if and only if the charge of the capacitor is constant. This happens when the capacitor has been (dis)charging for a long time, or when the circuit reaches steady state.

Last edited: Jan 20, 2008
6. Jan 20, 2008

### fatcat39

the problem says that the currents reach equilibrium. isn't that steady state?