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title: "An experimental non-Ohmic circuit element carries a current \\(I\\) related to the potential difference \\(V\\) across its terminals by the relationship \\(I = kV^3\\), where \\(k\\) is a positive empirical constant with appropriate units. Which of the following correctly pairs the differential resistance \\(\\dfrac{dV}{dI}\\) of the element as a function of \\(I\\) with the functional dependence of the power \\(P\\) dissipated by the element on \\(I\\)?"
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url: "https://nerd-notes.com/ubq/124796/"
date_modified: "2026-09-28T14:11:19+00:00"
---

# An experimental non-Ohmic circuit element carries a current \(I\) related to the potential difference \(V\) across its terminals by the relationship \(I = kV^3\), where \(k\) is a positive empirical constant with appropriate units. Which of the following correctly pairs the differential resistance \(\dfrac{dV}{dI}\) of the element as a function of \(I\) with the functional dependence of the power \(P\) dissipated by the element on \(I\)?

An experimental non-Ohmic circuit element carries a current \(I\) related to the potential difference \(V\) across its terminals by the relationship \(I = kV^3\), where \(k\) is a positive empirical constant with appropriate units. Which of the following correctly pairs the differential resistance \(\dfrac{dV}{dI}\) of the element as a function of \(I\) with the functional dependence of the power \(P\) dissipated by the element on \(I\)?

- **A.** \(\dfrac{dV}{dI} = \dfrac{1}{3k^{1/3}I^{2/3}}\) ; \(P \propto I^{4/3}\)
- **B.** \(\dfrac{dV}{dI} = \dfrac{1}{k^{1/3}I^{2/3}}\) ; \(P \propto I^{4/3}\)
- **C.** \(\dfrac{dV}{dI} = \dfrac{1}{3k^{1/3}I^{2/3}}\) ; \(P \propto I^2\)
- **D.** \(\dfrac{dV}{dI} = 3k^{1/3}I^{2/3}\) ; \(P \propto I^4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124796/*