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title: "A series circuit consists of an ideal battery of electromotive force (emf) \\(\\varepsilon = 12\\text{ V}\\), a resistor of resistance \\(R = 3.0\\text{ k}\\Omega\\), an open switch, and an uncharged capacitor of unknown capacitance \\(C\\). At time \\(t = 0\\text{ s}\\), the switch is closed, and a current sensor records the current \\(I\\) in the circuit as a function of time \\(t\\), as shown in the graph. Based on the graph, what is the capacitance \\(C\\) of the capacitor?"
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url: "https://nerd-notes.com/ubq/120444/"
date_modified: "2026-08-23T04:34:47+00:00"
---

# A series circuit consists of an ideal battery of electromotive force (emf) \(\varepsilon = 12\text{ V}\), a resistor of resistance \(R = 3.0\text{ k}\Omega\), an open switch, and an uncharged capacitor of unknown capacitance \(C\). At time \(t = 0\text{ s}\), the switch is closed, and a current sensor records the current \(I\) in the circuit as a function of time \(t\), as shown in the graph. Based on the graph, what is the capacitance \(C\) of the capacitor?

A series circuit consists of an ideal battery of electromotive force (emf) \(\varepsilon = 12\text{ V}\), a resistor of resistance \(R = 3.0\text{ k}\Omega\), an open switch, and an uncharged capacitor of unknown capacitance \(C\). At time \(t = 0\text{ s}\), the switch is closed, and a current sensor records the current \(I\) in the circuit as a function of time \(t\), as shown in the graph. Based on the graph, what is the capacitance \(C\) of the capacitor?

![A 2D quantitative graph with gridlines. The horizontal axis is labeled Time \(t\text{ (ms)}\) with major ticks and numerical labels at \(0\), \(3.0\), \(6.0\), \(9.0\), \(12.0\), \(15.0\), \(18.0\), \(21.0\), and \(24.0\). The vertical axis is labeled Current \(I\text{ (mA)}\) with major ticks and numerical labels at \(0\), \(1.0\), \(2.0\), \(3.0\), \(4.0\), and \(5.0\). Light gray gridlines align with all major tick marks. A single smooth solid black curve starts at \((0, 4.0)\) on the vertical axis, decays exponentially downward to the right, passes through the point \((6.0, 1.5)\), continues through \((12.0, 0.5)\), and asymptotically approaches \(0\text{ mA}\) near \(t = 24.0\text{ ms}\). A small filled circle marks the data point at \((6.0, 1.5)\). No other curves, labels, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459687-QF8xvQ.jpg)

- **A.** \(0.50\text{ }\mu\text{F}\)
- **B.** \(1.0\text{ }\mu\text{F}\)
- **C.** \(2.0\text{ }\mu\text{F}\)
- **D.** \(4.0\text{ }\mu\text{F}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120444/*