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title: "A non-ohmic circuit element has the current-versus-potential difference ( (I\\) vs. \\(V\\)) characteristic curve shown in the graph. At operating point \\(P\\), the potential difference across the element is \\(V_0 = 4.0\\text{ V}\\) and the current through it is \\(I_0 = 2.0\\text{ mA}\\). The dashed line is tangent to the curve at point \\(P\\) and intersects the horizontal axis at \\(V = 2.0\\text{ V}\\). Which of the following statements correctly relates the features of the graph to the resistance properties of the element at point \\(P\\)?"
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url: "https://nerd-notes.com/ubq/121561/"
date_modified: "2026-08-23T05:24:02+00:00"
---

# A non-ohmic circuit element has the current-versus-potential difference (
(I\) vs. \(V\)) characteristic curve shown in the graph. At operating point \(P\), the potential difference across the element is \(V_0 = 4.0\text{ V}\) and the current through it is \(I_0 = 2.0\text{ mA}\). The dashed line is tangent to the curve at point \(P\) and intersects the horizontal axis at \(V = 2.0\text{ V}\). Which of the following statements correctly relates the features of the graph to the resistance properties of the element at point \(P\)?

A non-ohmic circuit element has the current-versus-potential difference (
(I\) vs. \(V\)) characteristic curve shown in the graph. At operating point \(P\), the potential difference across the element is \(V_0 = 4.0\text{ V}\) and the current through it is \(I_0 = 2.0\text{ mA}\). The dashed line is tangent to the curve at point \(P\) and intersects the horizontal axis at \(V = 2.0\text{ V}\). Which of the following statements correctly relates the features of the graph to the resistance properties of the element at point \(P\)?

![A Cartesian coordinate graph with a horizontal axis labeled V (V) and a vertical axis labeled I (mA). The horizontal axis has numerical tick marks at 0, 2.0, and 4.0. The vertical axis has numerical tick marks at 0, 1.0, and 2.0. A smooth, solid curve begins at the origin (0, 0) and curves upward with increasing slope, passing through a marked point labeled P at coordinates (4.0, 2.0). A dashed straight line is tangent to the curve at point P, extending downward to intersect the horizontal axis at 2.0 and extending slightly past point P toward the upper right. Light dashed projection lines connect point P horizontally to 2.0 on the vertical axis and vertically to 4.0 on the horizontal axis. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462642-hDXBIi.jpg)

- **A.** The dynamic resistance is equal to the static resistance because Ohm's law applies directly at any instantaneous operating point on the curve, giving a value of \(2000\text{ }\Omega\).
- **B.** The dynamic resistance is \(2000\text{ }\Omega\) because dynamic resistance is determined by the slope of the secant line connecting the origin to point \(P\).
- **C.** The dynamic resistance is greater than the static resistance because the tangent line at point \(P\) has a steeper slope than the secant line connecting the origin to point \(P\).
- **D.** The dynamic resistance is \(1000\text{ }\Omega\), which is less than the static resistance of \(2000\text{ }\Omega\), because dynamic resistance is the reciprocal of the slope of the tangent line at point \(P\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121561/*