---
title: "A non-linear circuit element and a resistor of resistance \\(R = 5.0 \\text{ }\\Omega\\) are connected in series across an ideal battery of electromotive force \\(\\mathcal{E} = 12 \\text{ V}\\). For positive potential differences, the current \\(I\\) through the non-linear element is related to the potential difference \\(V_D\\) across it by \\(I = b V_D^2\\), where \\(b = 0.50 \\text{ A/V}^2\\). What is the electrical power dissipated by the non-linear element?"
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url: "https://nerd-notes.com/ubq/118459/"
date_modified: "2026-08-04T08:10:16+00:00"
---

# A non-linear circuit element and a resistor of resistance \(R = 5.0 \text{ }\Omega\) are connected in series across an ideal battery of electromotive force \(\mathcal{E} = 12 \text{ V}\). For positive potential differences, the current \(I\) through the non-linear element is related to the potential difference \(V_D\) across it by \(I = b V_D^2\), where \(b = 0.50 \text{ A/V}^2\). What is the electrical power dissipated by the non-linear element?

A non-linear circuit element and a resistor of resistance \(R = 5.0 \text{ }\Omega\) are connected in series across an ideal battery of electromotive force \(\mathcal{E} = 12 \text{ V}\). For positive potential differences, the current \(I\) through the non-linear element is related to the potential difference \(V_D\) across it by \(I = b V_D^2\), where \(b = 0.50 \text{ A/V}^2\). What is the electrical power dissipated by the non-linear element?

![A single-loop circuit schematic oriented horizontally. On the left vertical branch, an ideal battery is drawn with long and short parallel lines, labeled \mathcal{E} = 12 \text{ V}, with the positive terminal on top. The top horizontal wire connects the top of the battery to a resistor labeled R = 5.0 \ \Omega. The right vertical branch contains a non-linear circuit element represented by a rectangular box labeled D. The bottom horizontal wire completes the single closed loop back to the negative terminal of the battery. No other components, meters, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831016-Xjp3at.jpg)

- **A.** \(0.80 \text{ W}\)
- **B.** \(1.6 \text{ W}\)
- **C.** \(2.0 \text{ W}\)
- **D.** \(4.0 \text{ W}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118459/*