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

• Course Home
• Syllabus
• Electric Fields

  • 1. Introduction to Electric Fields
  • 2. Math Review, Fields
  • 3. Electric Fields and Discrete Charge Distributions
  • 4. Electric Fields and Continuous Charge Distributions
  • 5. Gauss's Law
• Electric Potential

  • 6. Discrete and Continuous Distributions of Charge
  • 7. Equipotential Lines and Electric Fields
  • 8. Gauss's Law and Configuration Energy
• Capacitors

  • 9. Conductors and Insulators, Conductors as Shields
  • 10. Capacitance and Capacitors, Energy Stored in Capacitors
  • 11. Capacitors and Dielectrics
• Circuits

  • 12. Current, Current Density, Resistance, and Ohm's Law
  • 13. Batteries and Circuit Elements
  • 14. DC Circuits
  • 15. DC Circuits with Capacitors
• Magnetic Fields and Forces

  • 16. Magnetic Field
  • 17. Magnetic Forces
  • 18. Magnetic Dipoles
• Creating Magnetic Fields

  • 19. Biot-Savart Law
  • 20. Ampere's Law
• Faraday's Law

  • 21. Faraday's Law
  • 22. Inductance and Magnetic Energy
  • 23. RL Circuits
• Oscillating Circuits

  • 24. Undriven RLC Circuits
  • 25. Driven RLC Circuits
• Maxwell's Equations

  • 26. The Displacement Current and Maxwell's Equations
  • 27. Poynting Vector and Energy Flow in a Capacitor
• Electromagnetic Waves

  • 28. Maxwell's Equations and Electromagnetic Waves
  • 29. Energy and Momentum in Electromagnetic Waves
  • 30. Generating EM Waves, Dipole Radiation and Polarization
• Nature of Light

  • 31. Interference
  • 32. Diffraction
• Download Course Materials

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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

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?

Problem 2: The Electric Field and Resistivity of a Wire

The potential difference between points a and b on a long wire is V_ab 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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