Electrical Potential Energy

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Section 1 Electric PotentialChapter 17

Electrical Potential Energy

• Electrical potential energy is potential energy associated with a charge due to its position in an electric field.

• Electrical potential energy is a component of mechanical energy.

ME = KE + PEgrav + PEelastic + PEelectric




Electrical Potential Energy, continued

• Electrical potential energy can be associated with a charge in a uniform field.

• Electrical Potential Energy in a Uniform Electric Field

PEelectric = –qEdelectrical potential energy = –(charge) (electric field strength)

(displacement from the reference point in the direction of the field)



Chapter 17

Electrical Potential Energy

Section 1 Electric Potential




Potential Difference

• Electric Potential equals the work that must be performed against electric forces to move a charge from a reference point to the point in question, divided by the charge.

• The electric potential associated with a charge is the electric energy divided by the charge:

V

PEelectric

q




Potential Difference, continued

• Potential Difference equals the work that must be performed against electric forces to move a charge between the two points in question, divided by the charge.

• Potential difference is a change in electric potential.

change in electric potential energy

potential differenceelectric charge

electricPEV

q



Chapter 17

Potential Difference

Section 1 Electric Potential





• The potential difference in a uniform field varies with the displacement from a reference point.

• Potential Difference in a Uniform Electric Field

∆V = –Ed

potential difference = –(magnitude of the electric field displacement)




Sample ProblemPotential Energy and Potential Difference

A charge moves a distance of 2.0 cm in the direction of a uniform electric field whose magnitude is 215 N/C.As the charge moves, its electrical potential energy decreases by 6.9 10-

19 J. Find the charge on the moving particle. What is the potential difference between the two locations?




Sample Problem, continuedPotential Energy and Potential Difference

Given:

∆PEelectric = –6.9 10–19 J

d = 0.020 m

E = 215 N/C

Unknown:

q = ?

∆V = ?





Use the equation for the change in electrical potential energy.

PEelectric = –qEd

Rearrange to solve for q, and insert values.

–19

–19

(–6.9 10 J)– –

(215 N/C)(0.020 m)

1.6 10 C

electricPEq

Ed

q





The potential difference is the magnitude of E times the displacement.

– –(215 N/C)(0.020 m)

–4.3 V

V Ed

V





• At right, the electric poten-tial at point A depends on the charge at point B and the distance r.

• An electric potential exists at some point in an electric field regardless of whether there is a charge at that point.




Potential Difference, continued• The reference point for potential difference near a

point charge is often at infinity.

• Potential Difference Between a Point at Infinity and a Point Near a Point Charge

• The superposition principle can be used to calculate the electric potential for a group of charges.

value of the point chargepotential difference = Coulomb constant

distance to the point charge

C

qV k

r



Chapter 17Section 1 Electric Potential

Superposition Principle and Electric Potential



Section 2 CapacitanceChapter 17

Capacitors and Charge Storage

• A capacitor is a device that is used to store electrical potential energy.

• Capacitance is the ability of a conductor to store energy in the form of electrically separated charges.

• The SI units for capacitance is the farad, F, which equals a coulomb per volt (C/V)




Capacitors and Charge Storage, continued

• Capacitance is the ratio of charge to potential difference.

magnitude of charge on each platecapacitance =

potential difference

QC

V



Chapter 17

Capacitance

Section 2 Capacitance





• Capacitance depends on the size and shape of a capacitor.

• Capacitance for a Parallel-Plate Capacitor in a Vacuum

–12 2

0

0

area of one of the platescapacitance = permittivity of a vacuum

distance between the plates

of the medium 8.85 10 C /N mpermittivity

AC

d





• The material between a capacitor’s plates can change its capacitance.

• The effect of a dielectric is to reduce the strength of the electric field in a capacitor.



Chapter 17

Capacitors in Keyboards




Chapter 17

Parallel-Plate Capacitor





Energy and Capacitors

• The potential energy stored in a charged capacitor depends on the charge and the potential difference between the capacitor’s two plates.

1electrical potential energy = (charge on one plate)(final potential difference)

2

1

2electricPE Q V




Sample ProblemCapacitance

A capacitor, connected to a 12 V battery, holds 36 µC of charge on each plate. What is the capacitance of the capacitor? How much electrical potential energy is stored in the capacitor?

Given:

Q = 36 µC = 3.6 10–5 C

∆V = 12 V

Unknown:

C = ? PEelectric = ?



Chapter 17

Sample Problem, continuedCapacitance

To determine the capacitance, use the definition of capacitance.

–5

–6

3.6 10 C

12 V

3.0 10 F 3.0 µF

QC

V

C




Chapter 17

Sample Problem, continuedCapacitance

To determine the potential energy, use the alternative form of the equation for the potential energy of a charged capacitor:

2

–6 2

–4

1( )

21

(3.0 10 F)(12 V)2

2.2 10 J

electric

electric

electric

PE C V

PE

PE




Section 3 Current and ResistanceChapter 17

Current and Charge Movement

• Electric current is the rate at which electric charges pass through a given area.

charge passing through a given area

electric current = time interval

QI

t



Chapter 17

Conventional Current

Section 3 Current and Resistance




Drift Velocity

• Drift velocity is the the net velocity of a charge carrier moving in an electric field.

• Drift speeds are relatively small because of the many collisions that occur when an electron moves through a conductor.



Chapter 17

Drift Velocity





Resistance to Current

• Resistance is the opposition presented to electric current by a material or device.

• The SI units for resistance is the ohm (Ω) and is equal to one volt per ampere.

• Resistance

potential difference

resistancecurrent

VR

I




Resistance to Current, continued

• For many materials resistance is constant over a range of potential differences. These materials obey Ohm’s Law and are called ohmic materials.

• Ohm’s low does not hold for all materials. Such materials are called non-ohmic.

• Resistance depends on length, cross-sectional area, temperature, and material.



Chapter 17

Factors that Affect Resistance





Resistance to Current, continued

• Resistors can be used to control the amount of current in a conductor.

• Salt water and perspiration lower the body's resistance.

• Potentiometers have variable resistance.



Section 4 Electric PowerChapter 17

Sources and Types of Current

• Batteries and generators supply energy to charge carriers.

• Current can be direct or alternating.– In direct current, charges move in a single

direction.– In alternating current, the direction of charge

movement continually alternates.




Energy Transfer

• Electric power is the rate of conversion of electrical energy.

• Electric power

P = I∆V

Electric power = current potential difference



Chapter 17

Energy Transfer

Section 4 Electric Power




Energy Transfer, continued

• Power dissipated by a resistor

• Electric companies measure energy consumed in kilowatt-hours.

• Electrical energy is transferred at high potential differences to minimize energy loss.

22 ( )V

P I V I RR



Chapter 17

Relating Kilowatt-Hours to Joules

Section 4 Electric Power

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Electrical Potential Energy