---
title: "A circuit consists of an ideal battery of voltage \\(\\mathcal{E}\\), a fixed resistor of resistance \\(R\\), and a thermistor connected in series, as shown. The thermistor has a negative temperature coefficient, meaning its resistance \\(R_{th}\\) decreases as its temperature increases. At time \\(t = 0\\), the thermistor is at room temperature with resistance \\(R_{th}(0) = R\\). As current flows for \\(t > 0\\), Joule heating causes the thermistor’s temperature to rise until it reaches thermal equilibrium with its surroundings at a steady-state current \\(I_{ss}\\). Which of the following graphs best represents the current \\(I\\) in the circuit as a function of time \\(t\\)?"
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url: "https://nerd-notes.com/ubq/118418/"
date_modified: "2026-08-04T08:09:58+00:00"
---

# A circuit consists of an ideal battery of voltage \(\mathcal{E}\), a fixed resistor of resistance \(R\), and a thermistor connected in series, as shown. The thermistor has a negative temperature coefficient, meaning its resistance \(R_{th}\) decreases as its temperature increases. At time \(t = 0\), the thermistor is at room temperature with resistance \(R_{th}(0) = R\). As current flows for \(t > 0\), Joule heating causes the thermistor’s temperature to rise until it reaches thermal equilibrium with its surroundings at a steady-state current \(I_{ss}\). Which of the following graphs best represents the current \(I\) in the circuit as a function of time \(t\)?

A circuit consists of an ideal battery of voltage \(\mathcal{E}\), a fixed resistor of resistance \(R\), and a thermistor connected in series, as shown. The thermistor has a negative temperature coefficient, meaning its resistance \(R_{th}\) decreases as its temperature increases. At time \(t = 0\), the thermistor is at room temperature with resistance \(R_{th}(0) = R\). As current flows for \(t > 0\), Joule heating causes the thermistor's temperature to rise until it reaches thermal equilibrium with its surroundings at a steady-state current \(I_{ss}\). Which of the following graphs best represents the current \(I\) in the circuit as a function of time \(t\)?

![A single-loop circuit schematic oriented horizontally. On the left vertical branch, an ideal battery is shown with its positive terminal at the top, labeled \mathcal{E}. The top horizontal wire connects to a fixed resistor labeled R. On the right vertical branch, a thermistor symbol (a resistor symbol with a diagonal line through it) is labeled R_{th}. The bottom horizontal wire connects the thermistor back to the negative terminal of the battery. An arrow above the top wire points to the right, labeled I(t). No other labels, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830997-t5E8qt.jpg)

- **A.** Graph A
- **B.** Graph B
- **C.** Graph C
- **D.** Graph D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118418/*