---
title: "Two nonideal batteries, Battery 1 with emf \\(\\mathcal{E}_1 = 2\\mathcal{E}_0\\) and internal resistance \\(r_1 = r\\), and Battery 2 with emf \\(\\mathcal{E}_2 = \\mathcal{E}_0\\) and internal resistance \\(r_2 = r\\), are connected in parallel with their positive terminals connected to the same upper conductor wire. A load resistor of resistance \\(R = 2r\\) is connected in parallel across the two batteries. Let \\(V_{T1}\\) and \\(V_{T2}\\) represent the terminal voltages of Battery 1 and Battery 2, respectively, and let \\(I_1\\), \\(I_2\\), and \\(I_3\\) represent the magnitudes of the currents through Battery 1, Battery 2, and resistor \\(R\\), respectively.  | Option | Terminal Voltage \\(V_{T1}\\) | Terminal Voltage \\(V_{T2}\\) | Current Magnitudes | | :— | :— | :— | :— | | (A) | \\(V_{T1} < \\mathcal{E}_1\\) | \\(V_{T2}  I_2 > I_3\\) | | (B) | \\(V_{T1} > \\mathcal{E}_1\\) | \\(V_{T2}  I_3 > I_2\\) | | (C) | \\(V_{T1} < \\mathcal{E}_1\\) | \\(V_{T2}  I_3 > I_2\\) | | (D) | \\(V_{T1}  \\mathcal{E}_2\\) | \\(I_1 > I_3 > I_2\\) |  Which row in the table correctly compares the terminal voltages \\(V_{T1}\\) and \\(V_{T2}\\) to their respective emfs and correctly ranks the magnitudes of the branch currents \\(I_1\\), \\(I_2\\), and \\(I_3\\)?"
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url: "https://nerd-notes.com/ubq/117505/"
date_modified: "2026-08-04T06:52:25+00:00"
---

# Two nonideal batteries, Battery 1 with emf \(\mathcal{E}_1 = 2\mathcal{E}_0\) and internal resistance \(r_1 = r\), and Battery 2 with emf \(\mathcal{E}_2 = \mathcal{E}_0\) and internal resistance \(r_2 = r\), are connected in parallel with their positive terminals connected to the same upper conductor wire. A load resistor of resistance \(R = 2r\) is connected in parallel across the two batteries. Let \(V_{T1}\) and \(V_{T2}\) represent the terminal voltages of Battery 1 and Battery 2, respectively, and let \(I_1\), \(I_2\), and \(I_3\) represent the magnitudes of the currents through Battery 1, Battery 2, and resistor \(R\), respectively.

| Option | Terminal Voltage \(V_{T1}\) | Terminal Voltage \(V_{T2}\) | Current Magnitudes |
| :— | :— | :— | :— |
| (A) | \(V_{T1} < \mathcal{E}_1\) | \(V_{T2}  I_2 > I_3\) |
| (B) | \(V_{T1} > \mathcal{E}_1\) | \(V_{T2}  I_3 > I_2\) |
| (C) | \(V_{T1} < \mathcal{E}_1\) | \(V_{T2}  I_3 > I_2\) |
| (D) | \(V_{T1}  \mathcal{E}_2\) | \(I_1 > I_3 > I_2\) |

Which row in the table correctly compares the terminal voltages \(V_{T1}\) and \(V_{T2}\) to their respective emfs and correctly ranks the magnitudes of the branch currents \(I_1\), \(I_2\), and \(I_3\)?

Two nonideal batteries, Battery 1 with emf \(\mathcal{E}_1 = 2\mathcal{E}_0\) and internal resistance \(r_1 = r\), and Battery 2 with emf \(\mathcal{E}_2 = \mathcal{E}_0\) and internal resistance \(r_2 = r\), are connected in parallel with their positive terminals connected to the same upper conductor wire. A load resistor of resistance \(R = 2r\) is connected in parallel across the two batteries. Let \(V_{T1}\) and \(V_{T2}\) represent the terminal voltages of Battery 1 and Battery 2, respectively, and let \(I_1\), \(I_2\), and \(I_3\) represent the magnitudes of the currents through Battery 1, Battery 2, and resistor \(R\), respectively.

| Option | Terminal Voltage \(V_{T1}\) | Terminal Voltage \(V_{T2}\) | Current Magnitudes |
| :--- | :--- | :--- | :--- |
| (A) | \(V_{T1} < \mathcal{E}_1\) | \(V_{T2} < \mathcal{E}_2\) | \(I_1 > I_2 > I_3\) |
| (B) | \(V_{T1} > \mathcal{E}_1\) | \(V_{T2} < \mathcal{E}_2\) | \(I_1 > I_3 > I_2\) |
| (C) | \(V_{T1} < \mathcal{E}_1\) | \(V_{T2} < \mathcal{E}_2\) | \(I_1 > I_3 > I_2\) |
| (D) | \(V_{T1} < \mathcal{E}_1\) | \(V_{T2} > \mathcal{E}_2\) | \(I_1 > I_3 > I_2\) |

Which row in the table correctly compares the terminal voltages \(V_{T1}\) and \(V_{T2}\) to their respective emfs and correctly ranks the magnitudes of the branch currents \(I_1\), \(I_2\), and \(I_3\)?

![A rectangular circuit schematic consisting of three parallel vertical branches connected by top and bottom horizontal wires. The left branch contains Battery 1, shown as an ideal voltage source symbol labeled \(\mathcal{E}_1 = 2\mathcal{E}_0\) in series with an internal resistor symbol labeled \(r_1 = r\); the positive long bar of the voltage source is at the top. The middle branch contains Battery 2, shown as an ideal voltage source symbol labeled \(\mathcal{E}_2 = \mathcal{E}_0\) in series with an internal resistor symbol labeled \(r_2 = r\); the positive long bar is also at the top. The right branch contains a load resistor symbol labeled \(R = 2r\). Arrow labels indicate branch currents: \(I_1\) in the left branch, \(I_2\) in the middle branch, and \(I_3\) in the right branch. No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826344-Rxtxwu.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117505/*