---
title: "A capacitor with capacitance \\(C = 20\\text{ }\\mu\\text{F}\\) is initially charged to a potential difference \\(V_0\\) and stores an initial electrical energy \\(U_0\\). At time \\(t = 0\\), a switch is closed to connect the capacitor in series with a resistor of resistance \\(R = 50\\text{ k}\\Omega\\), allowing the capacitor to discharge. What is the time \\(t\\) required for the energy stored in the capacitor to decrease to \\(25\\%\\) of its initial value \\(U_0\\)?"
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url: "https://nerd-notes.com/ubq/121595/"
date_modified: "2026-08-23T05:24:13+00:00"
---

# A capacitor with capacitance \(C = 20\text{ }\mu\text{F}\) is initially charged to a potential difference \(V_0\) and stores an initial electrical energy \(U_0\). At time \(t = 0\), a switch is closed to connect the capacitor in series with a resistor of resistance \(R = 50\text{ k}\Omega\), allowing the capacitor to discharge. What is the time \(t\) required for the energy stored in the capacitor to decrease to \(25\%\) of its initial value \(U_0\)?

A capacitor with capacitance \(C = 20\text{ }\mu\text{F}\) is initially charged to a potential difference \(V_0\) and stores an initial electrical energy \(U_0\). At time \(t = 0\), a switch is closed to connect the capacitor in series with a resistor of resistance \(R = 50\text{ k}\Omega\), allowing the capacitor to discharge. What is the time \(t\) required for the energy stored in the capacitor to decrease to \(25\%\) of its initial value \(U_0\)?

![A single rectangular circuit loop oriented with horizontal top and bottom wires and vertical left and right wires. The left vertical wire contains a capacitor labeled C represented by two parallel horizontal plates. The top horizontal wire contains a single-pole single-throw open switch labeled S. The right vertical wire contains a zigzag resistor labeled R. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462653-5lndM0.jpg)

- **A.** \(0.35\text{ s}\)
- **B.** \(0.69\text{ s}\)
- **C.** \(1.4\text{ s}\)
- **D.** \(2.8\text{ s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121595/*