notes/education/computer engineering/ECE2290/Ch 7, RL RC Circuits.md

Given an RL circuit, it starts with an initial condition.

KVL defines a first order homogeneous ordinary differential equation with constant coefficients:

 
	L \frac{di(t)}{dt} + Ri(t) = 0
	\to
L \frac{di(t)}{dt} = -Ri(t)

Steps for solving RC natural response circuits:

1. Determine the initial inductor current, I_0, by analyzing the circuit for t < 0.

2. Calculate the time constant, \tau RC, where R is the equivalent resistance connected to the capacitor for t \ge 0.

3. Write the equation for the capacitor voltage:

v(t) = V_o ^{e - \frac{t}{\tau}}, t \ge 0

4. Calculate other quantities of interest using the capacitor voltage