vault backup: 2026-08-31 11:12:38
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@@ -8,6 +8,7 @@ $$
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\to
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L \frac{di(t)}{dt} = -Ri(t)
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$$
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Steps for solving RC natural response circuits:
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1. Determine the initial inductor current, $I_0$, by analyzing the circuit for $t < 0$.
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@@ -15,4 +16,9 @@ Steps for solving RC natural response circuits:
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3. Write the equation for the capacitor voltage:
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$$ v(t) = V_o ^{e - \frac{t}{\tau}}, t \ge 0 $$
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4. Calculate other quantities of interest using the capacitor voltage
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4. Calculate other quantities of interest using the capacitor voltage
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- The *natural* response of a circuit is where there is an initial condition, but nothing else is driving the circuit.
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- The *step* response of a circuit describes the behavior of a circuit when a sudden change is introduced (switch toggled, et cetera)
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