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title: "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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url: "https://nerd-notes.com/ubq/125038/"
date_modified: "2026-09-28T14:13:30+00:00"
---

# 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?

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?

![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.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604809-kqeD9v.jpg)

- **A.** \( \dfrac{1}{9} \)
- **B.** \( \dfrac{1}{3} \)
- **C.** \( 1 \)
- **D.** \( 3 \)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125038/*