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title: "An ideal current source delivering a constant total current \\(I_0\\) is connected in parallel with an uncharged capacitor of capacitance \\(C\\) and a resistor of resistance \\(R\\) at time \\(t = 0\\). Which of the following expressions correctly gives the potential difference \\(V(t)\\) across the capacitor as a function of time \\(t\\) for \\(t \\ge 0\\)?"
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url: "https://nerd-notes.com/ubq/118368/"
date_modified: "2026-08-04T08:09:44+00:00"
---

# An ideal current source delivering a constant total current \(I_0\) is connected in parallel with an uncharged capacitor of capacitance \(C\) and a resistor of resistance \(R\) at time \(t = 0\). Which of the following expressions correctly gives the potential difference \(V(t)\) across the capacitor as a function of time \(t\) for \(t \ge 0\)?

An ideal current source delivering a constant total current \(I_0\) is connected in parallel with an uncharged capacitor of capacitance \(C\) and a resistor of resistance \(R\) at time \(t = 0\). Which of the following expressions correctly gives the potential difference \(V(t)\) across the capacitor as a function of time \(t\) for \(t \ge 0\)?

![A schematic diagram of a parallel circuit. On the left vertical branch, a circle with a single arrow pointing upward inside it is labeled I_0. Connected in parallel to its right across top and bottom horizontal wire rails are two vertical branches: the middle branch contains a zigzag resistor labeled R, and the rightmost branch contains two parallel vertical lines representing a capacitor labeled C. No other components or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830983-GsipTH.jpg)

- **A.** \(V(t) = I_0 R e^{-t/(RC)}\)
- **B.** \(V(t) = I_0 R \left(1 + e^{-t/(RC)}\right)\)
- **C.** \(V(t) = I_0 R \left(1 - e^{-2t/(RC)}\right)\)
- **D.** \(V(t) = I_0 R \left(1 - e^{-t/(RC)}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118368/*