# 15. DC Circuits with Capacitors

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## Learning Objectives

• To be able to include capacitors as one of our circuit elements, and to know how the electric potential changes across capacitors.
• To be able to calculate the currents in multi-loop circuits including capacitors using Kirchoff's Laws.
• To comprehend the nature of the differential equation describing a charging and discharging capacitor, and to be able to write down solutions to those equations.
• To be able to explain the meaning of the RC time constant, and how you would measure it.
• To be able to explain the power balance in a circuit where a capacitor is charging and in a circuit where it is discharging.

## Preparation

### Course Notes

Read through the course notes before watching the video.  The course note files may also contain links to associated animations or interactive simulations.

Direct-Current Circuits (PDF)

## Lecture Video

### Video Excerpts

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## Learning Activities

### Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF)

### Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems.

### Concept Questions

Concept Questions (PDF)

Solutions (PDF)

### Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

## Problem Solving Help

Watch the Problem Solving Help video for insights on how to approach and solve problems related to the concepts in this module.

### Problem: Discharging a Capacitor

A capacitor is charged to a potential of 15 V and is then connected to a voltmeter having an internal resistance of 2.25 MΩ. After a time of 5 s, the voltmeter reads 5 volts. What is the capacitance?

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