---
title: "A non-ohmic circuit element has a voltage-current relationship given by \\(V_D = C I^3\\), where \\(C\\) is a positive constant with appropriate units and \\(I\\) is the electric current through the element. The element is connected in series with a resistor of resistance \\(R\\) across an ideal battery of electromotive force \\(\\mathcal{E}_0\\). When the circuit carries a steady current \\(I_0\\), which of the following pairs of expressions correctly represents the total thermal power dissipated in the circuit, \\(P_{\\text{total}}\\), and the ratio of the power dissipated in the non-ohmic element to the power dissipated in the resistor, \\(\\dfrac{P_D}{P_R}\\)?"
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url: "https://nerd-notes.com/ubq/118443/"
date_modified: "2026-08-04T08:10:07+00:00"
---

# A non-ohmic circuit element has a voltage-current relationship given by \(V_D = C I^3\), where \(C\) is a positive constant with appropriate units and \(I\) is the electric current through the element. The element is connected in series with a resistor of resistance \(R\) across an ideal battery of electromotive force \(\mathcal{E}_0\). When the circuit carries a steady current \(I_0\), which of the following pairs of expressions correctly represents the total thermal power dissipated in the circuit, \(P_{\text{total}}\), and the ratio of the power dissipated in the non-ohmic element to the power dissipated in the resistor, \(\dfrac{P_D}{P_R}\)?

A non-ohmic circuit element has a voltage-current relationship given by \(V_D = C I^3\), where \(C\) is a positive constant with appropriate units and \(I\) is the electric current through the element. The element is connected in series with a resistor of resistance \(R\) across an ideal battery of electromotive force \(\mathcal{E}_0\). When the circuit carries a steady current \(I_0\), which of the following pairs of expressions correctly represents the total thermal power dissipated in the circuit, \(P_{\text{total}}\), and the ratio of the power dissipated in the non-ohmic element to the power dissipated in the resistor, \(\dfrac{P_D}{P_R}\)?

![A single-loop circuit schematic drawn with crisp rectangular wire paths. On the left vertical branch is an ideal DC battery labeled \(\mathcal{E}_0\) with its positive terminal at the top. On the top horizontal branch is an ideal resistor labeled \(R\). On the right vertical branch is a non-ohmic circuit component drawn as a square box labeled with the relation \(V_D = C I^3\). A clockwise current arrow labeled \(I_0\) is indicated near the top wire. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-circuit-1-1785831007-jiX9zh.jpg)

- **A.** Total power: \(P_{\text{total}} = I_0^2 R + C I_0^3\) Power ratio: \(\dfrac{P_D}{P_R} = \dfrac{C I_0}{R}\)
- **B.** Total power: \(P_{\text{total}} = I_0^2 R + C I_0^3\) Power ratio: \(\dfrac{P_D}{P_R} = \dfrac{C I_0^2}{R}\)
- **C.** Total power: \(P_{\text{total}} = I_0^2 R + C I_0^4\) Power ratio: \(\dfrac{P_D}{P_R} = \dfrac{C I_0^3}{R}\)
- **D.** Total power: \(P_{\text{total}} = I_0^2 R + C I_0^4\) Power ratio: \(\dfrac{P_D}{P_R} = \dfrac{C I_0^2}{R}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118443/*