# 12. Current, Current Density, Resistance, and Ohm's Law

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## Learning Objectives

• To be able to explain the concept of current and current density, and to know how to obtain one given the other.
• To be able to explain a simple model for resistivity, and to be able to calculate the resistance of resistors with simple geometries.
• To be able to recognize when Ohm's Law will hold, and to be able to describe the meaning of Ohm's Law when it does hold.
• To be able to give examples of situations where Ohm's Law does not hold.

## 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.

Current and Resistance (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 (PDF)

Solutions (PDF)

### Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

## Problem Solving Help

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

### Problem 1: Current and Current Density

A total of 72 Coulombs of charge is transmitted by a silver wire 1.3 mm in diameter over a time of 1 hour and 10 minutes. What is the current in the wire and the current density in the wire? If silver contains 5.8x1028 free electrons per cubic meter, what is the drift velocity of the electrons in the wire?

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» iTunes U (MP4 - 11MB)
» Internet Archive (MP4 - 11MB)

### Problem 2: The Electric Field and Resistivity of a Wire

The potential difference between points a and b on a long wire is Vab Volts. The two points are l meters apart. What is the electric field in the wire? If the current density in the wire is J, what is the resistivity ρ of the wire?

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