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AP Physics C: E&M
13.5 Circuits with Resistors and Inductors (LR Circuits)
13.4 Inductance
AdvancedMCQMathematicalProportional Analysis24.7k
Two circuit schematics arranged side by side, labeled Scenario 1 on the left and Scenario 2 on the right. In Scenario 1, a single rectangular loop contains an inductor labeled L on the left vertical branch, a resistor labeled R_1 on the top horizontal wire, and a resistor labeled R_2 on the right vertical branch. A single curved arrow along the wire indicates initial current I_0. In Scenario 2, an inductor labeled L is on the left vertical branch, connected across top and bottom horizontal wires to two parallel vertical branches to its right: the first contains resistor labeled R_1, and the second contains resistor labeled R_2. An arrow near the inductor indicates initial current I_0. All circuit wires are drawn as thin solid black lines on a white background. No other labels, lines, text, or axes appear.
Circuits for the discharge of the inductor in Scenario 1 and Scenario 2.
An ideal inductor with inductance \(L\) carries an initial steady current \(I_0\). In Scenario 1, the inductor is disconnected from its power supply and allowed to discharge through two resistors with resistances \(R_1 = R\) and \(R_2 = 3R\) connected in series. In Scenario 2, the same inductor carrying the same initial current \(I_0\) is allowed to discharge through the two resistors connected in parallel. What is the ratio \(\Delta E_{1,\text{parallel}} / \Delta E_{1,\text{series}}\) of the total thermal energy dissipated in resistor \(R_1\) in Scenario 2 to that in Scenario 1 after all current has decayed to zero?

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