---
title: "A circuit is constructed using an ideal battery with potential difference \\(\\Delta V_0\\), an open switch, a resistor of resistance \\(R\\), and an initially uncharged capacitor of capacitance \\(C\\), all connected in series. The switch is closed at time \\(t = 0\\). Which of the following correctly describes the current \\(I\\) through the resistor and the potential difference \\(V_C\\) across the capacitor as functions of time \\(t\\) for \\(t > 0\\), and provides a valid justification?"
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url: "https://nerd-notes.com/ubq/117377/"
date_modified: "2026-08-04T06:52:01+00:00"
---

# A circuit is constructed using an ideal battery with potential difference \(\Delta V_0\), an open switch, a resistor of resistance \(R\), and an initially uncharged capacitor of capacitance \(C\), all connected in series. The switch is closed at time \(t = 0\). Which of the following correctly describes the current \(I\) through the resistor and the potential difference \(V_C\) across the capacitor as functions of time \(t\) for \(t > 0\), and provides a valid justification?

A circuit is constructed using an ideal battery with potential difference \(\Delta V_0\), an open switch, a resistor of resistance \(R\), and an initially uncharged capacitor of capacitance \(C\), all connected in series. The switch is closed at time \(t = 0\). Which of the following correctly describes the current \(I\) through the resistor and the potential difference \(V_C\) across the capacitor as functions of time \(t\) for \(t > 0\), and provides a valid justification?

![A schematic diagram of a single-loop DC circuit oriented as a rectangle. On the left vertical branch is an ideal battery labeled \(\Delta V_0\) with the longer positive terminal on top. On the top horizontal branch is an open switch S. On the right vertical branch is a resistor labeled R. On the bottom horizontal branch is an uncharged capacitor labeled C. Connecting wires complete the rectangular loop. No other labels or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826320-FmY7en.jpg)

- **A.** The current \(I\) increases exponentially while \(V_C\) increases exponentially, because charge accumulates on the capacitor plates at a constant rate over time.
- **B.** The current \(I\) increases exponentially while \(V_C\) decreases exponentially, because electric potential energy is continuously transferred from the capacitor to the resistor.
- **C.** The current \(I\) remains constant while \(V_C\) increases linearly, because the ideal battery supplies a constant current regardless of the charge on the capacitor.
- **D.** The current \(I\) decreases exponentially while \(V_C\) increases exponentially, because as charge accumulates on the capacitor, its increasing potential difference opposes the battery voltage, reducing the net current in the circuit.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117377/*