vault backup: 2026-11-07 10:54:53

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

@@ -1,22 +0,0 @@
-
-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
-
-- The *natural* response of a circuit is where there is an initial condition, but nothing else is driving the circuit.
-- The *step* response of a circuit describes the behavior of a circuit when a sudden change is introduced (switch toggled, et cetera)