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:
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:
The full derivation, if you're interested:
We can use the integrating factor = :
Defining at :
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?
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y = 10e^{-x}