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title: "Circuit 1 contains an inductor of inductance \\(L_0\\) and a resistor of resistance \\(R_0\\), while Circuit 2 contains an inductor of inductance \\(2L_0\\) and a resistor of resistance \\(2R_0\\). Both circuits are connected to identical ideal batteries of electromotive force \\(\\mathcal{E}_0\\) for a time \\(t \\gg \\tau\\), where \\(\\tau = \\dfrac{L_0}{R_0}\\) is their common inductive time constant. At time \\(t = 0\\), the battery in each circuit is instantaneously removed and replaced with an ideal conducting wire, allowing each inductor to discharge through its connected resistor. Which circuit initially stores a greater magnetic energy just before \\(t = 0\\), and which circuit experiences a greater peak rate of Joule heating in its resistor during the discharge?"
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url: "https://nerd-notes.com/ubq/125047/"
date_modified: "2026-09-28T14:13:38+00:00"
---

# Circuit 1 contains an inductor of inductance \(L_0\) and a resistor of resistance \(R_0\), while Circuit 2 contains an inductor of inductance \(2L_0\) and a resistor of resistance \(2R_0\). Both circuits are connected to identical ideal batteries of electromotive force \(\mathcal{E}_0\) for a time \(t \gg \tau\), where \(\tau = \dfrac{L_0}{R_0}\) is their common inductive time constant. At time \(t = 0\), the battery in each circuit is instantaneously removed and replaced with an ideal conducting wire, allowing each inductor to discharge through its connected resistor. Which circuit initially stores a greater magnetic energy just before \(t = 0\), and which circuit experiences a greater peak rate of Joule heating in its resistor during the discharge?

Circuit 1 contains an inductor of inductance \(L_0\) and a resistor of resistance \(R_0\), while Circuit 2 contains an inductor of inductance \(2L_0\) and a resistor of resistance \(2R_0\). Both circuits are connected to identical ideal batteries of electromotive force \(\mathcal{E}_0\) for a time \(t \gg \tau\), where \(\tau = \dfrac{L_0}{R_0}\) is their common inductive time constant. At time \(t = 0\), the battery in each circuit is instantaneously removed and replaced with an ideal conducting wire, allowing each inductor to discharge through its connected resistor. Which circuit initially stores a greater magnetic energy just before \(t = 0\), and which circuit experiences a greater peak rate of Joule heating in its resistor during the discharge?

![Two separate rectangular circuit schematics drawn side-by-side in grayscale, labeled Circuit 1 on the left and Circuit 2 on the right. Circuit 1 consists of a single loop with an ideal battery of emf \(\mathcal{E}_0\) on the left vertical branch, a single-pole double-throw switch at the top, an inductor of inductance \(L_0\) depicted as four rounded semicircular loops on the right vertical branch, and a resistor of resistance \(R_0\) depicted as four sharp zig-zags on the bottom horizontal branch. Circuit 2 has an identical rectangular topology to the right, showing an ideal battery of emf \(\mathcal{E}_0\) on the left vertical branch, a switch at the top, an inductor labeled \(2L_0\) on the right vertical branch, and a resistor labeled \(2R_0\) on the bottom branch. No other labels, text, lines, or meters appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604818-UMxg0D.jpg)

- **A.** Greater initial stored energy: Circuit 2; Greater peak rate of Joule heating: Circuit 2
- **B.** Greater initial stored energy: Circuit 2; Greater peak rate of Joule heating: Circuit 1
- **C.** Greater initial stored energy: Circuit 1; Greater peak rate of Joule heating: Circuit 1
- **D.** Greater initial stored energy: Circuit 1; Greater peak rate of Joule heating: Circuit 2

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/125047/*