1. Honors Physics

2. Electrical Potential Energy PE associated with a charge due to its position in an electric field. Analogous to PE g PE g of an object results from its position in a gravitational field (mgh) Is a component of mechanical energy ME = KE + PE grav + PE elastic + PE electric

3. Similarity of PE electric and PE g PE g = mgh m is mass g is gravitational field (a g ) h is distance above a reference point PE elect = -qEd q is charge E is electric field strength d is component of displacement in the direction of the electric field from reference point Using dimensional analysis, what is the unit of PE elect ?

4. Electric Work Whenever a force moves an object, work is done on the object. When an electric force moves a charge, work is done on that charge. It is the electric field, E, that exerts force on a charge Therefore, the electric field, E, does work on a charge. This results in a change in PE elect.

5. Electric PE in a Uniform Electric Field A uniform field is one that has the same magnitude and direction at all points, such as between two parallel plates Remember: electric field lines are always directed from away from positive and toward negative

6. Electric Potential Energy Recall that ΔPE = -W When charge q is released at point a, electric force will move the charge to b, i.e. The electric field does work on the charge q

7. Electric Potential Energy W = Fd Since F = qE(remember E = F/q) W = qEd PE b -PE a = -qEd ΔPE = -qEd Significance of the (-) sign: PE elect Increases if charge is (-) Decreases if charge is (+)

8. PE as a charge moves in a uniform electric field Movement of charge+ charge- charge Along ELoses PEGains PE Opposite EGains PELoses PE ΔPE = -qEd Negative sign indicates that PE will increase if the charge is negative and decrease if the charge is positive

9. Potential Difference Electric potential (V) is the ratio of PE elect to charge q Represents the work needed to move a charge against electric forces from a reference point to some other point in an electric field, divided by the charge The SI units of electric potential are what? Which is a …?

10. Potential difference The change in electric potential The difference in electrical potential between two points Is the work that must be done against electric forces to move a charge from one point to another divided by the charge Is the change in energy per unit charge

11. Potential Difference Unit is the volt (V) Remember: PE elect is a quantity of energy Electrical potential is a measure of energy per unit charge Potential difference describes change in energy per unit charge

12. Potential Difference in a Uniform Electric Field Varies in a uniform field with displacement from a reference point Where d is displacement parallel to the field Use this equation to determine potential difference between two points in a field

13. Potential Difference at a Point Near a Charge One point is near the charge The other point is at infinity

14. Electric potential due to multiple charges Electric potentials are scalar quantities (whew!) So…. Total potential at some point in a field is the simple sum of the potentials due to each charge Keep track of signs!

15. Sample Problem As a charge moves x a = 4.0 cm to x b = 6.0 cm in a uniform field of 350 N/C, it loses 4.5 x 10 -16 J of potential energy. What is the magnitude of the charge? 6.4 x 10 -17 C What is the potential difference between the two points a and b? -7.0V

16. 17.2 Capacitance Capacitors are devices that store electrical PE Often constructed of parallel metal plates When connected to a battery, the plates become charged When fully charged, ∆V cap = ∆V bat

17. Schematic Representation of a Capacitor and Battery Intro to Capacitor

18. Construction of a Capacitor Parallel plates Parallel plates separated by an insulator (dielectric material) rolled into a cylinder saves space

19. Capacitance Ability of a conductor to store energy in the form of separated charges Unit of capacitance is the Farad, named for Michael Faraday 1F = 1C/V 1 Farad is a large amount of capacitance so… Often use pF, nF, or µF Supplemental instruction on capacitance View on your own, ~ 17 min.

20. Capacitance of a Parallel-Plate Capacitor in a Vacuum When no material exists between the plates ε 0 is the permittivity of the medium between the plates A measure of ability to develop an electrical field, permitting transfer of charges ε 0 in a vaccuum is 8.85 x 10 -12 C 2 /Nm 2

21. Dielectric Materials Materials placed between the plates of a capacitor can increase capacitance. Typically these are insulating materials

22. Dielectric Constants (K) Dielectric materials have different values of “dielectric constant” (K). Increase capacitance

23. Performance of Dielectric Materials Molecules of the dielectric are polarizable As charge builds on the capacitor plates, dielectric molecules orient to the electric field This effectively reduces the charge on the plates…. allowing more charge to be carried by each plate

24. Capacitor Discharge The opposite of charging, releasing stored charge Electrical potential of the capacitor is used to do electrical work such as … The flash of a camera Signaling the stroke of a computer keyboard

25. Capacitance of a Sphere R is radius Because the earth has a large radius, it has a very large capacitance i.e., the earth can accept or supply a very large amount of charge without changing its electrical potential This is why the earth is “ground,” (reference point for measuring potential differences)

26. Energy and Capacitors Because work is done to move charges to and from opposite plates… A charged capacitor holds electrical potential energy PE stored in a charged capacitor is equal to the (–) work done to charge it

27. Breakdown voltage Voltage at which discharge begins, i.e. charges move

28. Energy and Capacitors PE Stored in a Charged Capacitor

29. Current and Resistance Current is the rate of movement of charge Rate of movement of electrons through a cross- sectional area

30. Sample Problem If current flowing through a light bulb is 0.835 A, how long does it take for 1.67 C of charge to pass through the filament of the bulb? 2.00 seconds

31. Conventional Direction of Current Depending upon the circumstances, either positive, negative, or both can move. Particles that move are called charge carriers By convention, direction of current is defined as the direction a positive charge moves or would move if it could. In metals, only electrons can move. Good conductors permit charge carriers to move easily Electrons in metals Ions in solution (electrolytes)

32. Conventional Direction of Current

33. Drift Velocity Recall the structure of metals Valence electrons move about randomly due to their thermal energy Their net movement is zero But if an electric field is established in the wire, there is a net movement of electrons against the electric field (toward +) Drift velocity animation http://www.bbc.co.uk/staticarchive/4e6786539008e5012ff9c723c4255ae6fc6c1b9f.gif

34. Drift Velocity It is the electric field that exerts force and thereby sets charge carriers in motion E propagates very rapidly (near speed of light) Charge carriers move more slowly, in an erratic path, Called drift velocity Slow: e.g. in a copper wire carrying a 10.0 A current, v drift = 0.246 mm/s Consider motion of an electron through a wire

35. Resistance to Current Opposition to electric current Unit of electrical resistance is the ohm (Ω) More commonly known as Ohm’s law

36. Ohmic and Non-ohmic Materials Materials which follow ohm’s law are ohmic materials Resistance is constant over a wide range of potential differences (linear) Non-ohmic materials have variable resistance (non-linear) Diodes are constructed of non- ohmic materials

37. Other Factors Affecting Resistance

38. Function of Resistance From Ohm’s Law, changing resistance can change current So, if current needs to be reduced in a circuit, you can increase the resistance In many cases, ∆V is constant, so changing resistance is the only option for reducing current.

39. Electrical Resistance in the Body Electrical resistance is reduced as the body becomes wet or sweats This is due to the greater availability of ions to conduct current Practical applications: Your body is more susceptible increased current when wet Lie detectors EKGs, etc

40. Potentiometers Devices that have variable resistance “Pots” Applications Control knobs on electronic devices Stereos, dimmer switches, joy sticks, etc.

41. 17.4 Electric Power A potential difference (∆V) is necessary to cause current (I) Batteries supply chemical energy (PE chem ) which can be converted into electical PE Generators convert mechanical energy into electrical PE E.g. hydroelectric power plants Coal or natural gas powr plants Nuclear power plants

42. Direct and Alternating Current DC current flows in one direction only Electrons move toward the (+) terminal Conventional current directed from (+) to (-) AC current Terminals of source of ΔV constantly switch Causing constant reversal of current, e.g. 60 Hz Rapid switching causes e - s to vibrate rather than have a net motion.

43. DC and AC DC constant uni-directional AC not constant bi-directional

44. Energy Transfer In a DC circuit Electrons leave the battery with high PE Lose PE as flow through the circuit Regain PE when returned to battery (battery supplies PE through electrochemical reactions)

45. Electric Power The rate of conversion of electrical energy SI unit is the watt (W)

46. Other Formulas for Power

47. Kilowatt-hours How utility companies measure energy consumed Is the energy delivered in one hour a constant rate of one kW 1kWh=3.6 x 10 6 J What is the cost to light a 100 W light bulb for 1 full day if the electric utility rate is $0.0600 per kWh?

48. Transmission Lines Transit at high voltage and low current to minimize energy lost during transmission P=I 2 R