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

AP Physics C Mrs. Coyle

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**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.

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**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).

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**Cu and Zinc Electrodes. Why?**

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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

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**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

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**Direct Current DC Alternating Current AC Provided by batteries**

Provided by power companies

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**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.

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

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**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.

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**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.

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

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**A Battery Provides Energy**

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

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**Resistors use up Energy**

When the current goes through the resistor it goes to a lower potential. Electric Circuit

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**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

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**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

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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?

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**Question: Why is the bird on the wire safe?**

Question: Why do electricians work with one hand behind their back?

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**Question: Why is the ground prong longer than the other two in a plug?**

Question: Why is there a third rail for the subway?

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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)

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**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.

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Resistor An object that has a given resistance.

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**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

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**Nonohmic Material, Graph**

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

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**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

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**Which has the greatest and least resistance?**

Ans: Greatest-D, Smallest-B

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**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)

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**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

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**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

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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

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**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

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**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

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**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

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**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

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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:

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**Derivation of Ohm’s Law**

+ + + + + + a b

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**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

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**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

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