PS 250: Lecture 11 Stored Energy and Dielectrics

J. B. Snively September 23, 2015

Today’s Class

Energy Storage in Capacitors Dielectrics and Breakdown Summary

Energy Storage

Capacitors store energy (via charge), and can maintain a potential difference even after the

original voltage source is removed.

The energy stored in a capacitor can be calculated by equating it with the work required to charge that capacitor to

some potential difference.

Energy StorageWork required to transfer infinitesimal charge “dq”:

dW = �V dq =q

Cdq

Work required to charge from q=0 to q=Q:

W =� Q

0

q

Cdq =

Q2

2C

Potential energy stored in the charged capacitor = = Work required to charge capacitor =

U =Q2

2C=

12Q�V

And Since Q = C�V U =

12C(�V )2

Today’s Class

Energy Storage in Capacitors Dielectrics and Breakdown Summary

Dielectric Properties

Insulating materials (“Dielectrics”) have different properties, which can be quantified by their permittivity relative to free space.

Insulating materials have a “Dielectric strength”, or maximum electric field threshold, beyond which they begin to conduct via breakdown.

Effects on Permittivity and Capacitance

d

Area = A+Q

-Q

+

-V

Dielectric Material� = ��o

C =�A

d= �

�oA

d= �Co

Capacitance dependent on modified dielectric constant:

Capacitance SummaryCapacitance is a property of electrodes, defining their ability to store charge given an applied potential difference.

Capacitors carrying stored charge also therefore store energy, which may be released (perhaps rapidly!)

Properties determined by the dielectric material between the conductors, which vary in permittivity and breakdown threshold.

Summary / Next Class:

Mastering Physics Due Wednesday

Homework Due Friday

Begin Reading Chapter 25!