10. Capacitance and Capacitors, Energy Stored in Capacitors

• 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 define what we mean by capacitance C and to explain why it is a useful concept in terms of energy storage of electric fields.
• To be able to calculate the capacitance of a parallel plate capacitor and of other capacitors with high degrees of symmetry.
• To outline why energy is stored in capacitors by describing the process by which capacitors are charged and why that process requires an amount of energy given by Q2/2C.

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.

Read sections 5.1 through 5.4:
Capacitance and Dielectrics (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

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: Parallel Plate Capacitor

The plates of a parallel plate capacitor are a distance d apart. The plates have an area A. Calculate the capacitance of this capacitor.

Problem 2: Capacitors in Series and in Parallel

A circuit contains capacitors in series and in parallel. Find the charge on each capacitor and potential difference across each capacitor.

Problem 3: Capacitance of a Spherical Capacitor

A spherical capacitor is formed from a solid metallic sphere of radius R₁ surrounded by a spherical conducting shell of radius R₂. Find the capacitance of this arrangement.

Problem 4: Parallel Plate Capacitor with a Variable Gap

A parallel plate capacitor begins with a distance between the plates of d₁. If there is no battery in the circuit, what happens to the potential between the plates when we decrease d₁ to d₂, with d₂ < d₁? What happens to the energy stored in the capacitor when this transition takes place? Now, connect the capacitor to a battery. Answer the same questions for this situation as you did for the previous case.

Related Visualizations

The visualizations linked below are related to the concepts covered in this module.

• The Capacitor
• The Electrostatic Force Experiment

 

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