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education/computer engineering/ECE2290/Ch 7, RL RC Circuits.md
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@@ -8,6 +8,7 @@ $$
\to \to
L \frac{di(t)}{dt} = -Ri(t) L \frac{di(t)}{dt} = -Ri(t)
$$ $$
Steps for solving RC natural response circuits: Steps for solving RC natural response circuits:
1. Determine the initial inductor current, $I_0$, by analyzing the circuit for $t < 0$. 1. Determine the initial inductor current, $I_0$, by analyzing the circuit for $t < 0$.
@@ -16,3 +17,8 @@ Steps for solving RC natural response circuits:
3. Write the equation for the capacitor voltage: 3. Write the equation for the capacitor voltage:
$$ v(t) = V_o ^{e - \frac{t}{\tau}}, t \ge 0 $$ $$ v(t) = V_o ^{e - \frac{t}{\tau}}, t \ge 0 $$
4. Calculate other quantities of interest using the capacitor voltage 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)