---
title: "An ideal battery of emf \\(\\varepsilon\\) is connected across a potentiometer of total resistance \\(R\\). A sliding contact (wiper) is positioned at the midpoint, dividing the potentiometer into two equal sections, each of resistance \\(R/2\\). A load resistor of resistance \\(R_L = R\\) is then connected between the wiper and the bottom terminal of the potentiometer. What is the output voltage \\(V_{\\text{out}}\\) across the load resistor, and how does \\(V_{\\text{out}}\\) compare to the unloaded output voltage \\(V_{\\text{unloaded}}\\) measured at the midpoint before the load resistor was attached?"
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url: "https://nerd-notes.com/ubq/118394/"
date_modified: "2026-08-04T08:09:53+00:00"
---

# An ideal battery of emf \(\varepsilon\) is connected across a potentiometer of total resistance \(R\). A sliding contact (wiper) is positioned at the midpoint, dividing the potentiometer into two equal sections, each of resistance \(R/2\). A load resistor of resistance \(R_L = R\) is then connected between the wiper and the bottom terminal of the potentiometer. What is the output voltage \(V_{\text{out}}\) across the load resistor, and how does \(V_{\text{out}}\) compare to the unloaded output voltage \(V_{\text{unloaded}}\) measured at the midpoint before the load resistor was attached?

An ideal battery of emf \(\varepsilon\) is connected across a potentiometer of total resistance \(R\). A sliding contact (wiper) is positioned at the midpoint, dividing the potentiometer into two equal sections, each of resistance \(R/2\). A load resistor of resistance \(R_L = R\) is then connected between the wiper and the bottom terminal of the potentiometer. What is the output voltage \(V_{\text{out}}\) across the load resistor, and how does \(V_{\text{out}}\) compare to the unloaded output voltage \(V_{\text{unloaded}}\) measured at the midpoint before the load resistor was attached?

![A circuit schematic showing an ideal battery of emf \varepsilon on the left vertical branch with positive terminal on top. Wire extends from top of battery to the top terminal of a vertical potentiometer resistor of total resistance R. The potentiometer is split into two equal halves, each labeled R/2, separated by a central node with a sliding contact wiper. Wire extends from the wiper to the right, connecting to a vertical load resistor labeled R_L = R. The bottom of the load resistor and the bottom terminal of the potentiometer connect back to the negative terminal of the battery along a bottom horizontal wire. A voltage label V_out with a double-headed arrow is marked across the load resistor R_L. No other labels or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830993-WY8g3c.jpg)

- **A.** \(V_{\text{out}} = \dfrac{1}{3}\varepsilon\); \(V_{\text{out}} < V_{\text{unloaded}}\)
- **B.** \(V_{\text{out}} = \dfrac{2}{5}\varepsilon\); \(V_{\text{out}} < V_{\text{unloaded}}\)
- **C.** \(V_{\text{out}} = \dfrac{2}{5}\varepsilon\); \(V_{\text{out}} = V_{\text{unloaded}}\)
- **D.** \(V_{\text{out}} = \dfrac{1}{2}\varepsilon\); \(V_{\text{out}} = V_{\text{unloaded}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118394/*