Resistor-capacitor circuits are any configuration of a normal DC Circuit which includes a resistor (load) and a Capacitor. Due to the nature of capacitors, these circuits are time dependant.

Let’s start with a simple circuit involving a Battery, a resistor and a Capacitor:

Resistor-Capacitor Circuits .excalidraw

When a capacitor is introduced, the circuit now has an additional time dependency, because the current flowing through the capacitor (and hence, the circuit), is dependant on .

Analysis using Kirchhoff’s Law

Being a simple circuit with no junctions, we know the total current is constant, and we can use the conservation of energy:

and again, because there are no junctions:

However, for the capacitor, we use the formula for Capacitance and the formula for Current:

This equation is a Linear First Order ODE:

which evaluates to:

Since :

We also use tau to be the RC time constant:

Which, given constant voltage and resistance across the resistor, looks something like this:

#todo Finish with nice CSS and points?

left=0; right=3;
top=10; bottom=-1;
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y = 10e^{-x}