Electrical Energy & Current

1. Electrical Energy & Current Honors Physics

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

3. Gravitational Potential Energy Physicsclassroom.com

4. Similarity of PEelectric and PEg • PEg = mgh • m is mass • g is gravitational field (ag) • h is distance above a reference point • PEelect = -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 PEelect?

5. Electric Potential Energy & Work Physicsclassroom.com

6. Electric Potential Energy & Work Physicsclassroom.com

7. 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 PEelect.

8. 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

9. 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 • So, the PE of charge a decreases

10. Electric Potential Energy • W = Fd • Since F = qE (remember E = F/q) • W = qEd • PEb-PEa= -qEd • ΔPE = -qEd • Significance of the (-) sign: PEelect • Increases if charge is (-) • Decreases if charge is (+)

11. PE as a charge moves in a uniform electric field ΔPE = -qEd Negative sign indicates that PE will increase if the charge is negative and decrease if the charge is positive

12. Potential Energy between two charges

13. Learning check • When a negative charge moves in the direction of an electric field it gains PE (T/F). • When a positive charge moves against the electric field it loses PE (T/F) • In order for a negative charge to lose PE, it must move (with/against) the electric field. • The change in PE of a charge is equal to –qEd (T/F)

14. Potential Difference • Electric potential (V) is the ratio of PEelect 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 • W = Fd = qEd • The SI units of electric potential are what? Which is a …?

15. 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

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

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

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

19. Sample Problem • As a charge moves xa = 4.0 cm to xb = 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? • 3.2 x 10-17C • What is the potential difference between the two points a and b? • -14.0V

20. 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!

21. Summary of Formulas ΔPE = -qEd

22. 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, ∆Vcap = ∆Vbat

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

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

25. 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.

26. Capacitance of a Parallel-Plate Capacitor in a Vacuum • When no material exists between the plates • ε0 is the permittivity of the medium between the plates • A measure of ability to develop an electrical field, permitting transfer of charges • ε0 in a vaccuum is 8.85 x 10-12 C2/Nm2

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

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

29. 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

30. 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

31. 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)

32. 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

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

34. Energy and Capacitors PE Stored in a Charged Capacitor

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

36. 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

37. 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)

38. Conventional Direction of Current

39. 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 (for enrichment) http://www.bbc.co.uk/staticarchive/4e6786539008e5012ff9c723c4255ae6fc6c1b9f.gif

40. Drift Velocity Consider motion of an electron through a wire It is the electric field that exerts force and thereby sets charge carriers in motion (E = F/Q) 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, vdrift = 0.246 mm/s

41. Relationship of Voltage and Current: Conductance and Resistance http://s3.amazonaws.com/answer-board-image/c8b9a2d5-43d2-40b4-a578-1874d002386f.gif

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

43. 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

44. Other Factors Affecting Resistance

45. 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.

46. 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

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

48. 17.4 Electric Power • A potential difference (∆V) is necessary to cause current (I) • Batteries supply chemical energy (PEchem) which can be converted into PEelect • Generators convert mechanical energy into electrical Peelect • E.g. hydroelectric power plants • Wind turbines • Coal or natural gas power plants • Nuclear power plants • Solar power • Geothermal energy

49. 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.

50. DC and AC • DC • constant • uni-directional • AC • not constant • bi-directional