---
title: "A solar cell is modeled as an ideal emf \\(\\mathcal{E}_s\\) in series with an internal resistance \\(r_s\\). It is connected in a single closed loop to a battery modeled as an ideal emf \\(\\mathcal{E}_b\\) in series with an internal resistance \\(r_b\\), where \\(\\mathcal{E}_b > \\mathcal{E}_s\\). The positive terminal of the battery is connected to the positive terminal of the solar cell, and their negative terminals are connected together. Which of the following correctly pairs the current \\(I\\) in the circuit and the potential difference \\(V_s\\) across the terminals of the solar cell?"
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url: "https://nerd-notes.com/ubq/118426/"
date_modified: "2026-08-04T08:10:01+00:00"
---

# A solar cell is modeled as an ideal emf \(\mathcal{E}_s\) in series with an internal resistance \(r_s\). It is connected in a single closed loop to a battery modeled as an ideal emf \(\mathcal{E}_b\) in series with an internal resistance \(r_b\), where \(\mathcal{E}_b > \mathcal{E}_s\). The positive terminal of the battery is connected to the positive terminal of the solar cell, and their negative terminals are connected together. Which of the following correctly pairs the current \(I\) in the circuit and the potential difference \(V_s\) across the terminals of the solar cell?

A solar cell is modeled as an ideal emf \(\mathcal{E}_s\) in series with an internal resistance \(r_s\). It is connected in a single closed loop to a battery modeled as an ideal emf \(\mathcal{E}_b\) in series with an internal resistance \(r_b\), where \(\mathcal{E}_b > \mathcal{E}_s\). The positive terminal of the battery is connected to the positive terminal of the solar cell, and their negative terminals are connected together. Which of the following correctly pairs the current \(I\) in the circuit and the potential difference \(V_s\) across the terminals of the solar cell?

![A single rectangular circuit loop oriented vertically. The left vertical branch contains a battery represented by an ideal emf symbol labeled \mathcal{E}_b and a series internal resistor labeled r_b. The right vertical branch contains a solar cell represented by an ideal emf symbol labeled \mathcal{E}_s and a series internal resistor labeled r_s. The positive terminal of \mathcal{E}_b is at the top end of the left branch, and the positive terminal of \mathcal{E}_s is at the top end of the right branch. The top horizontal wire connects the top of the left branch to the top of the right branch. The bottom horizontal wire connects the bottom of the left branch to the bottom of the right branch. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831001-4vR2KO.jpg)

- **A.** \(I = \dfrac{\mathcal{E}_b + \mathcal{E}_s}{r_b + r_s}\) and \(V_s = \mathcal{E}_s - I r_s\)
- **B.** \(I = \dfrac{\mathcal{E}_b - \mathcal{E}_s}{r_b + r_s}\) and \(V_s = \mathcal{E}_s + I r_s\)
- **C.** \(I = \dfrac{\mathcal{E}_b - \mathcal{E}_s}{r_b + r_s}\) and \(V_s = \mathcal{E}_s - I r_s\)
- **D.** \(I = \dfrac{\mathcal{E}_b + \mathcal{E}_s}{r_b + r_s}\) and \(V_s = \mathcal{E}_s + I r_s\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118426/*