Fun with Capacitors

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

A simple Capacitor TWO PLATES WIRES Battery

INSIDE THE DEVICE

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

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

Device 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.

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 (Hold this thought.)

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!

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.

Size Matters! A Random Access Memory stores information on small capacitors which are either charged (bit=1) or uncharged (bit=0). Voltage across one of these capacitors ie either zero or the power source voltage (5.3 volts in this example). Typical capacitance is 55 fF (femto=10-15) Question: How many electrons are stored on one of these capacitors in the +1 state?

Small is better in the IC world!

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.