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 Alternating Current AC Provided by batteries
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?

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. Electrons flow in a net direction away from the (-) terminal.
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.

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

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

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 = A Δx
Total number of charge carriers= n A Δx

16. Current in terms of Drift Speed Iav = ΔQ/Δt = nqvdA or for a charge of an electron: Iav =nevdA
Derivation:
ΔQ = (nA Δx)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 The relationship between current and voltage is linear
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=ρ L 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 Temperature r= 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 a critical 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 /A J=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 Conductivity J = σ E
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)t For t=t the average time interval between successive collisions
vf avg = 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