Electrical Energy & Current

1. Electrical Energy & Current

2. 17.1 Introduction to Electric PE, Electric Potential, and Potential Difference • Intro to Electric Potential

3. 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

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

5. 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 • W = Fd • Since F = qE (E = F/q) • W = qEd • PEb-PEa= -qEd • ΔPE = -qEd

6. PE as a charge moves in a uniform electric field

7. Similarity of PEelectric and PEg • PEg = mgh • m is mass • g is gravitational field • h is distance above a reference point • PEelect = -qEd • q is charge • E is electric field strength • d is distance from reference point • The (-) sign indicates the PEelectwill increase for –q and decrease for +q • Using dimensional analysis, what is the unit of PEelect?

8. Potential Difference • Electric potential 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 • The unit of electric potential is what?

9. 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

10. Potential Difference • Unit is the volt (V)

11. 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

12. Potential Difference at a Point Near a Charge • One point is near the charge • The other point is at infinity • Use this equation to find the potential difference at a single point

13. 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!

14. Sample Problem • As a charge moves xa = 4.0 cm to xb = 8.0 cm in a uniform field of 350 N/C, it loses 4.5 x 10-18 J of potential energy. • What is the magnitude of the charge? • What is the potential difference between the two points a and b?

15. 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

16. Capacitance • Ability of a conductor to store energy in the form of separated charges • Unit of capacitance is the farad, F

17. Capacitance of a Parallel Plate Capacitor in a Vacuum • A is the area of the plates • E0 is permittivity constant for a vacuum • = 8.85 x 10-12 C2/Nm2

18. Dielectric Materials • Insulating material placed between the plates of a capacitor • Increases the ability of a capacitor to carry a charge

19. Discharging a Capacitor • Capacitors are devices that store charge • When discharge, they release charge • Computer keyboards are an example of capacitors in action

20. 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)

21. Energy and Capacitors PE Stored in a Charged Capacitor

22. 17.3 Current and Resistance • Current is the rate of movement of charge • Rate of movement of electrons through a cross-sectional area

23. 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

24. 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)

25. Conventional Direction of Current • Direction of conventional current is the direction a positive charge would travel, if it could move

26. Drift Velocity http://www.bbc.co.uk/staticarchive/4e6786539008e5012ff9c723c4255ae6fc6c1b9f.gif 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

27. 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, vdrift = 2.46 x 10-4 m/s Consider motion of an electron through a wire

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

29. 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

30. Other Factors Affecting Resistance

31. 17.4 Electric Power • A potential difference (∆V) is necessary to cause current (I) • Batteries supply chemical energy (PEchem) 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

32. 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 ∆V constantly switch • Causing constant reversal of current, e.g. 60 Hz • Rapid switching causes e-s to vibrate rather than have a net motion.

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

34. 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)

35. Internal structure of a dry cell http://static.sfdict.com/dictstatic/dictionary/graphics/ahsd/jpg/ASbatter.jpg

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

37. Other Formulas for Power

38. 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 106 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?

39. Transmission Lines Transit at high voltage and low current to minimize energy lost during transmission Compare the equations…. P = I2R P = I∆V