How to do RC Circuit with R and C in parallel

Here is a case where we have an RC circuit, but with a resistor and the capacitor in parallel with each other. This is tricky mathematically, but we can do it conceptually and only worry about numbers when t = 0 and after 'a long time.' Let's take a look.

How to Solve a Charging RC Circuit

RC circuits make up the next level of sophistication for us when it comes to circuits. We have done plain resistor circuits, plain capacitor circuits, and now RC circuits. Here is an example of how to find the charge as a function of time for a charging capacitor. It involves setting up a first-order differential equation for the circuit, and then solving that equation. In the end, we have exponential increase of charge on the capacitor, and exponential decay of current through the resistor and battery. Keep in mind the key is to write the equation for the circuit, and that depends on Kirchhoff's voltage rule, V = V(resistor) + V(capacitor).