-Electric Current -Resistance -Factors that affect resistance -Microscopic View of Current

1. -Electric Current -Resistance -Factors that affect resistance-Microscopic View of Current AP Physics C Mrs. Coyle

2. Remember: Electric Potential Energy Difference-Two Unlike Charges + Higher Potential Energy - Lower Potential Energy • To cause movement of a charge, there must be a potential difference.

3. Voltaic Cell (chemical cell, battery) • Alessandro Volta (1800’s) • Battery: device that converts chemical energy to electricity. • A battery provides a potential energy difference (voltage source).

4. Cu and Zinc Electrodes. Why?

5. Electric Current • Electric current is the rate of flow of charge through a cross sectional area • The SI unit of current is the ampere (A) • 1 A = 1 C / s • The symbol for electric current is I

6. Average Electric Current • ΔQ is the amount of charge that passes through A in time Δt • Assume charges are moving perpendicular to a surface of area A Instantaneous Electric Current

7. Direct Current • DC • Provided by batteries • Alternating Current • AC • Provided by power companies

8. Microscopic View of Current: • While the switch is open: Free electrons (conducting electrons) are always moving in random motion. • The random speeds are at an order of 106 m/s. The sharp changes in direction are due to collisions • There is no net movement of charge across a cross section of a wire.

9. What occurs in a wire when the circuit switch is closed? http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/imgele/micohm.gif

10. What occurs in a wire when the circuit switch is closed? • An electric field is established instantaneously (at almost the speed of light, 3x108 m/s). • Free electrons, while still randomly moving, immediately begin drifting due to the electric field, resulting in a net flow of charge. • Average drift velocity is about 0.01cm/s.

11. Closing the switch establishes a potential difference (voltage) and an electric field in the circuit. High Potential Low Potential • Electrons flow in a net direction away from the (-) terminal.

12. Conventional current has the direction that the (+) charges would have in the circuit. http://media-2.web.britannica.com/eb-media/36/236-004-D4AA985F.gif

13. Electric Circuit The battery “pumps” positive charges from low (-) to high (+) potential. A Battery Provides Energy

14. Electric Circuit When the current goes through the resistor it goes to a lower potential. Resistors use up Energy

15. Charge Carrier Density, n:number of charge carriers per unit volume • Charged particles (current carriers)move through a conductor of cross-sectional area A • Volume = AΔx • Total number of charge carriers= n AΔx

16. Current in terms of Drift SpeedIav = ΔQ/Δt = nqvdAor for a charge of an electron:Iav=nevdA Derivation: • ΔQ = (nAΔx)q • Drift speed, vd, is the speed at which the carriers move: vd = Δx / Δt • ΔQ = (nAvd Δt)q

17. Question: • If the drift velocity is about 0.01cm/s, why do the lights turn on instantaneously when the circuit switch is closed? • What is required in order to have an electric current flow in a circuit?

18. Question: Why is the bird on the wire safe? Question:Why do electricians work with one hand behind their back?

19. Question: Why is the ground prong longer than the other two in a plug? Question: Why is there a third rail for the subway?

20. Resistance, R • Resistance of an object to the flow of electrical current. • Resistance in a circuit is due to collisions between the electrons carrying the current with the fixed atoms inside the conductor • R= V / I • Resistance equals the ratio of voltage to current. • Unit: Ohm (Ω)

21. Ohm’s Law (Georg Ohm, 1787-1854) V = IR • The voltage , V, across a resistor is proportional to the current, I, that flows through it. • In general, resistance does not depend on the voltage. (but for non-Ohmic resistors it may.) • Applies to a given resistor or equivalent combination. • The voltage is the potential difference across the resistor or equivalent combination.

22. Resistor • An object that has a given resistance.

23. Ohmic Resistor • A device that obeys Ohm’s Law, who’s resistance does not depend on the voltage. • Most metals obey Ohm’s law • The relationship between current and voltage is linear

24. Nonohmic Material, Graph • Nonohmic materials are those whose resistance changes with voltage or current • The current-voltage relationship is nonlinear

25. Resistance • Depends on material, size and shape, temp. R=ρL A ρ: resistivity -Resistivity has SI units of ohm-meters (Ω. M -An ideal conductor would have zero resistivity σ: 1/ρ conductivity

26. Which has the greatest and least resistance? Ans: Greatest-D, Smallest-B

27. Temperature Dependence of Resistance and Resistivity for metals R= Ro(1 +αT) • Ro : reference resistance usually at 20oC (sometimes at 0o C) • α: temperature coefficient of resistivity Resistivity • r= r o(1 +αT)

28. Resistivity and Temperaturer= r o(1 +αT) • For metals, the resistivity is nearly proportional to temperature • Nonlinear region at very low temperatures • Resistivity reaches a finite value (residual resistivity) as the temperature approaches absolute zero

29. Semiconductors r= r o(1 +αT), a<0 • For semiconductors there is a decrease in resistivity with an increase in temperature • α is negative

30. Superconductors • For superconductors resistances fall to close to zero below acritical temperature TC • The graph is the same as a normal metal above TC, but suddenly drops to zero at TC

31. Current Density, J:current per unit area J = I / A • A current density J and an electric field E are established in a conductor, when a potential difference is applied across the conductor • The current density is a vector in the direction of the positive charge carriers

32. Current Density, J: current per unit area J = I / A = nqvdA /AJ=nqvd • J units: A/m2 • This expression is valid only if the current density is uniform and A is perpendicular to the direction of the current

33. Ohm’s Law in terms of ConductivityJ = σE • Ohm’s law states that for many materials, the ratio of the current density to the electric field is a constant σ(conductivity)that is independent of the electric field producing the current

34. Radial Resistance of a Cable,Example 27.4 • In a coaxial cable the current flows along its length. Some unwanted current leaks radially. Find the radial resistance of the silicon

35. Ex.27.4 Solution • Assume the silicon between the conductors to be concentric elements of thickness dr. • The total resistance across the entire thickness of silicon:

36. Derivation of Ohm’s Law + + + + + + a b

37. Derivation of Drift Velocity • Electrical force acting on electron is F = qE • a = F / me = qE / me • vf = vi + at • vf = vi + (qE/me)tFor t=t the average time interval between successive collisions • vfavg = vd • vd = (qE/me)t

38. Derivation of Resistivity J = nqvd = (nq2E / me)t J=sE • Note, the conductivity and the resistivity do not depend on the strength of the field • Mean free path, ℓ , average distance between collisions • t = ℓ/vav