Capacitance

Physics 102Professor Lee

CarknerLecture 13

PAL #12 Electric Potential

 

  sign of U sign of V sign of W naturally?

+ charge moves with E field    

       

+ charge moves against E field    

       

-charge moves with E field     

       

-charge moves against E field    

       

    

--

--

-

-+

++

+

++ Yes

Yes

No

No

Particle Motion

E

Low V

High V Increase U

Increase U

Decrease U

(natural)

Decrease U

(natural)

If a charge of value Q is at a point of potential V, we know,

A) The velocity of the charge at that pointB) The direction the charge will move inC) The amount of electrical potential

energy the charge hasD) The distance to the nearest other

chargeE) None of the above

If a charged particle moves along an equipotential line (assuming no other forces),

A) Its potential energy does not change

B) No work is doneC) Its kinetic energy does not changeD) Its velocity does not changeE) All of the above

When a charge +Q is placed at the corner of a square the potential at the center is 3 volts. What is the potential at the center if charges of +Q are placed on all corners of the square?

A) 0 VB) 3 VC) 9 VD) 12 VE) 24 V

Circuits What is the purpose of potential difference?

It makes charges move

e.g. light lightbulbs, induce movement in motors, move information etc.

We will examine the key components of electric circuits Up first, the capacitor

Capacitance A capacitor is a device that can store

charge and thus energy

The amount of charge depends on the potential difference across the capacitor and the intrinsic properties of the device This intrinsic property is called capacitance

and is represented by C

Capacitance Defined The amount of charge stored by a capacitor is just:

Or, defining the capacitance:

C = Q/V

The units of capacitance are farads (F)1 F = 1 C/V

Typical capacitances are much less than a farad:

e.g. microfarad = F = 1 X 10-6 F

Capacitor Info

Maintaining a potential difference across the plates causes the charge to separate

Electrons are repelled from the negative terminal and end up on one plate

Plates have a net charge Plates can’t touch or charge would jump across

Capacitor Diagram

--

+ +V VQ

Capacitor Properties The capacitance depends on four things:

The distance between them (d) The dielectric constant of the material between

the plates ()

The permittivity of free space (0) A constant: 0 = 8.85 X 10-12 C2/N m2

The total capacitance can be written as:C = 0(A/d)

Capacitance Dependence

s

Dielectric

The molecules in the material will align with the electric field

The polarized material partially cancels out the electric field between the plates reducing the voltage

A dielectric allows a capacitor to store more charge with the same voltage

Dielectrics

Dielectric Constant

The dielectric constant is a multiplicative factor for the capacitance C = C0

e.g.

The dielectric also allows you to move the plates closer together without touching

Breakdown The dielectric must be an insulator

If the voltage is large enough, the charge will jump across anyway

While Q = CV, there is a limit to how much we can increase Q by increasing V

Normally about 20 million volts

Energy in a Capacitor

Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch

Charge stops moving when the V across the plates is equal to the max V possible for the circuit

Charging a Capacitor

Total Energy

We find that the total energy stored in a capacitor is related to the charge and the final potential difference:

Energy = 1/2 Q V =1/2 C (V)2 = Q2/2C

Large C and large V produce large stored energy

Using Capacitors Generally only for short periods of time

Charge can bleed-off if capacitor is not perfectly insulated and potential is not maintained

Useful when you need a quick burst of energy

For a flash, capacitor is discharged into a gas (like xenon) that will glow when ionized

Since capacitance depends on d, can also use capacitance to measure separation

Next Time

Read 18.1-18.5, 18.8-18.9 Homework Ch 17, P: 44, 49, Ch 18,

P: 4, 26