Electric Current Resistance Factors that affect resistance Microscopic

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

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.

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

Cu and Zinc Electrodes. Why?

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

Average Electric Current n n 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

n Direct Current n DC n Provided by batteries n Alternating Current n AC n Provided by power companies

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

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

What occurs in a wire when the circuit switch is closed? n An electric field is established instantaneously (at almost the speed of light, 3 x 108 m/s). n Free electrons, while still randomly moving, immediately begin drifting due to the electric field, resulting in a net flow of charge. n Average drift velocity is about 0. 01 cm/s.

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

Conventional current has the direction that the (+) charges would have in the circuit. http: //media-2. web. britannica. com/eb-media/36/236 -004 -D 4 AA 985 F. gif

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

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

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

Current in terms of Drift Speed Iav = ΔQ/Δt = nqvd. A or for a charge of an electron: Iav =nevd. A Derivation: n ΔQ = (n. A Δx)q n Drift speed, vd, is the speed at which the carriers move: vd = Δx / Δt n ΔQ = (n. Avd Δt)q

Question: n If the drift velocity is about 0. 01 cm/s, why do the lights turn on instantaneously when the circuit switch is closed? n What is required in order to have an electric current flow in a circuit?

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

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

Resistance, R n n n 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)

Ohm’s Law (Georg Ohm, 1787 -1854) V = IR n n 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.

Resistor n An object that has a given resistance.

Ohmic Resistor n n n 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

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

Resistance n 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

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

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

Resistivity and Temperature r= r o(1 +α T) n n n 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

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

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

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

Current Density, J: current per unit area J = I / A = nqvd. A /A J=nqvd n n J units: A/m 2 This expression is valid only if the current density is uniform and A is perpendicular to the direction of the current

Ohm’s Law in terms of Conductivity J=σE n 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

Radial Resistance of a Cable, Example 27. 4 n In a coaxial cable the current flows along its length. Some unwanted current leaks radially. Find the radial resistance of the silicon

Ex. 27. 4 Solution n Assume the silicon between the conductors to be concentric elements of thickness dr. n The total resistance across the entire thickness of silicon:

Derivation of Ohm’s Law + + + a b

Derivation of Drift Velocity n Electrical force acting on electron is F = q. E n a = F / me = q. E / me vf = vi + at vf = vi + (q. E/me)t For t=t the average time interval between successive collisions vf avg = vd n n vd = (q. E/me)t

Derivation of Resistivity J = nqvd = (nq 2 E / me)t J=s. E n n n 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