source An RC Circuit is a circuit with a Capacitor and a Resistor.
For example:
(a) is the original state with an uncharged capacitor, (b) is the state where the capacitor is charging, and (c) is the state where the capacitor is being discharged.
We can find equations for charge and current at the capacitor during charging and discharging:
Charging:
Steps:
- Use Kirchhoff’s Laws to get an equation for the circuit
- Replace current and charge at resistor with values that can be used to take a derivative.
- Rearrange and integrate
- Simplify using
form
At the end, we simplified
We can use this new equation for charge to find Current as the capacitor charges:
We can model these two equations on a graph.
We get the bottom two equations by putting the equation in terms of
Discharging
We use a similar method for discharging
And then we turn that equation into the one for current:
