-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.

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 10 6 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.

What occurs in a wire when the circuit switch is closed?

An electric field is established instantaneously (at almost the speed of light, 3x10 8 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.

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?

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

Conventional current has the direction that the (+) charges would have in the circuit.

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).

Cu and Zinc Electrodes. Why?

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?

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

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

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

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

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

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

Current in terms of Drift Speed I av = ΔQ/Δt = nqv d A or for a charge of an electron: I av =nev d A Derivation: ΔQ = (nA Δx)q Drift speed, v d, is the speed at which the carriers move: v d = Δx / Δt ΔQ = (nAv d Δt)q

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)

Ohm’s Law (Georg Ohm, ) 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.

Resistor An object that has a given resistance.

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

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

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

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

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

Resistivity and Temperature  =  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

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

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

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

Current Density, J: current per unit area J = I / A = nqv d A /A J=nqv d 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 = 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

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

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:

Derivation of Ohm’s Law b a

Derivation of Drift Velocity Electrical force acting on electron is F = qE a = F / m e = qE / m e v f = v i + at v f = v i + (qE/m e )t For t=  the average time interval between successive collisions v f avg = v d v d = (qE/m e ) 

Derivation of Resistivity Note, the conductivity and the resistivity do not depend on the strength of the field Mean free path, ℓ, average distance between collisions  = ℓ /v av J = nqv d = (nq 2 E / m e )  J=  E