---
title: "An RC circuit consisting of a resistor of resistance \\(R\\) and an uncharged capacitor of capacitance \\(C\\) connected in series is driven by a variable voltage source producing a ramp voltage \\(V(t) = \\alpha t\\), where \\(\\alpha\\) is a positive constant and \\(t \\ge 0\\). Which of the following expressions represents the charge \\(q(t)\\) on the capacitor as a function of time?"
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url: "https://nerd-notes.com/ubq/118429/"
date_modified: "2026-08-04T08:10:01+00:00"
---

# An RC circuit consisting of a resistor of resistance \(R\) and an uncharged capacitor of capacitance \(C\) connected in series is driven by a variable voltage source producing a ramp voltage \(V(t) = \alpha t\), where \(\alpha\) is a positive constant and \(t \ge 0\). Which of the following expressions represents the charge \(q(t)\) on the capacitor as a function of time?

An RC circuit consisting of a resistor of resistance \(R\) and an uncharged capacitor of capacitance \(C\) connected in series is driven by a variable voltage source producing a ramp voltage \(V(t) = \alpha t\), where \(\alpha\) is a positive constant and \(t \ge 0\). Which of the following expressions represents the charge \(q(t)\) on the capacitor as a function of time?

![A schematic of a single-loop series RC circuit. On the left is a variable voltage source symbol labeled V(t) = \alpha t. Connected in series along the top wire is a resistor labeled R. Connected in series along the right vertical wire is a capacitor labeled C. Wires complete the loop back to the voltage source. No other elements or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831001-DbOWMd.jpg)

- **A.** \(q(t) = \alpha C t \left(1 - e^{-t / RC}\right)\)
- **B.** \(q(t) = \alpha C \left(t - RC e^{-t / RC}\right)\)
- **C.** \(q(t) = \alpha C \left(t - RC + RC e^{-t / RC}\right)\)
- **D.** \(q(t) = \alpha C \left(t + RC - RC e^{-t / RC}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118429/*