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title: "A circuit contains an ideal battery of emf \\(\\varepsilon = 18\\text{ V}\\), two resistors, an open switch, and an uncharged capacitor of capacitance \\(C = 10\\text{ }\\mu\\text{F}\\). At time \\(t = 0\\), the switch is closed, and the potential difference \\(V_C\\) across the capacitor is measured as a function of time \\(t\\), as shown in the graph. The dashed horizontal line represents the steady-state asymptote, and the dashed diagonal line is tangent to the curve at \\(t = 0\\). Based on the graph, what is the equivalent resistance of the circuit connected across the capacitor?"
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url: "https://nerd-notes.com/ubq/124974/"
date_modified: "2026-09-28T14:12:26+00:00"
---

# A circuit contains an ideal battery of emf \(\varepsilon = 18\text{ V}\), two resistors, an open switch, and an uncharged capacitor of capacitance \(C = 10\text{ }\mu\text{F}\). At time \(t = 0\), the switch is closed, and the potential difference \(V_C\) across the capacitor is measured as a function of time \(t\), as shown in the graph. The dashed horizontal line represents the steady-state asymptote, and the dashed diagonal line is tangent to the curve at \(t = 0\). Based on the graph, what is the equivalent resistance of the circuit connected across the capacitor?

A circuit contains an ideal battery of emf \(\varepsilon = 18\text{ V}\), two resistors, an open switch, and an uncharged capacitor of capacitance \(C = 10\text{ }\mu\text{F}\). At time \(t = 0\), the switch is closed, and the potential difference \(V_C\) across the capacitor is measured as a function of time \(t\), as shown in the graph. The dashed horizontal line represents the steady-state asymptote, and the dashed diagonal line is tangent to the curve at \(t = 0\). Based on the graph, what is the equivalent resistance of the circuit connected across the capacitor?

![A Cartesian graph with horizontal axis labeled t (ms) and vertical axis labeled V_C (V). The horizontal axis has tick marks and labels at 0, 2, 4, 6, 8, 10, 12, 14, and 16. The vertical axis has tick marks and labels at 0, 2, 4, 6, 8, 10, 12, and 14. Thin gray gridlines extend across the plot at each tick mark on both axes. A horizontal dashed line extends across the entire width of the grid at V_C = 12. A solid curve begins at the origin (0, 0), rises with decreasing slope, and asymptotically approaches the horizontal line V_C = 12 from below, passing near (4.2, 6) and (6, 7.6). A straight dashed line starts at the origin (0, 0) and extends upward to the right, passing through the grid intersection at (6, 12). No other lines, curves, points, or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604746-GS1BKj.jpg)

- **A.** \(280\text{ }\Omega\)
- **B.** \(420\text{ }\Omega\)
- **C.** \(600\text{ }\Omega\)
- **D.** \(900\text{ }\Omega\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124974/*