Capacitance PHY 2049 Chapter 25

Chapter 25 Capacitance In this chapter we will cover the following topics: -Capacitance C of a system of two isolated conductors. -Calculation of the capacitance for some simple geometries. -Methods of connecting capacitors (in series , in parallel). -Equivalent capacitance. -Energy stored in a capacitor. -Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor. -Gauss’ law in the presence of dielectrics. (25 - 1)

Capacitors

Capacitor Composed of two metal plates. Each plate is charged one positive one negative Stores energy SYMBOL

A simple Capacitor TWO PLATES WIRES Battery

INSIDE THE DEVICE

What is STORED in the capacitor? An Electric Field Energy Charge All three None of these

Two Charged Plates (Neglect Fringing Fields) Air or Vacuum Area A - Q +Q E V=Potential Difference Symbol ADDED CHARGE

Where is the charge? + + + + + - AREA=A s=Q/A + - Q +Q d Air or Vacuum V=Potential Difference

The capacitor therefore stores energy! One Way to Charge: Start with two isolated uncharged plates. Take electrons and move them from the + to the – plate through the region between. As the charge builds up, an electric field forms between the plates. You therefore have to do work against the field as you continue to move charge from one plate to another. The capacitor therefore stores energy!

Capacitor Demo

More on Capacitors - Q +Q d Air or Vacuum Area A E V=Potential Difference Gaussian Surface Same result from other plate!

DEFINITION - Capacity The Potential Difference is APPLIED by a battery or a circuit. The charge q on the capacitor is found to be proportional to the applied voltage. The proportionality constant is C and is referred to as the CAPACITANCE of the device.

UNITS A capacitor which acquires a charge of 1 coulomb on each plate with the application of one volt is defined to have a capacitance of 1 FARAD One Farad is one Coulomb/Volt

Continuing… The capacitance of a parallel plate capacitor depends only on the Area and separation between the plates. C is dependent only on the geometry of the device!

After the switch is closed, how much charge passed through the capacitor? V C/V V/C CV C+V

S P N (25 - 6)

Units of e0 pico

Simple Capacitor Circuits Batteries Apply potential differences Capacitors Wires Wires are METALS. Continuous strands of wire are all at the same potential. Separate strands of wire connected to circuit elements may be at DIFFERENT potentials.

NOTE Work to move a charge from one side of a capacitor to the other is = qEd. Work to move a charge from one side of a capacitor to the other is qV Thus qV = qEd E=V/d As before

TWO Types of Connections SERIES PARALLEL

Parallel Connection V CEquivalent=CE

Series Connection The charge on each capacitor is the same ! q -q q -q V C1 C2 q -q q -q The charge on each capacitor is the same !

Series Connection Continued V C1 C2 q -q q -q

More General

Example C1 C2 series (12+5.3)pf (12+5.3)pf V C3 C1=12.0 uf C2= 5.3 uf C3= 4.5 ud C1 C2 series (12+5.3)pf (12+5.3)pf V C3

More on the Big C +q -q E=e0A/d +dq We move a charge dq from the (-) plate to the (+) one. The (-) plate becomes more (-) The (+) plate becomes more (+). dW=Fd=dq x E x d

So….

Not All Capacitors are Created Equal Parallel Plate Cylindrical Spherical

Spherical Capacitor

Calculate Potential Difference V (-) sign because E and ds are in OPPOSITE directions.

Continuing… Lost (-) sign due to switch of limits.