current

Current and Resistance

Tuesday, July 19, 2011

Current

Convention : Current depicts flow of positive (+) charges


Current

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Area



Current

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Area

Ammeter(measures current)



Current

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Area


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Current

A measure of how much charge passes through an amount of time


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Current

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Count how many charges flow through


Current

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Expand surface to a volumeCount how many charges flow through


Current

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Expand surface to a volume

Area = A



Current

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Area = A length = Δx



Current

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Total volumeV = (A)(Δx)

length = ΔxArea = A



Current

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Number of charges = (charge density or charge per volume)*(volume)Number of charges = (n) * (AΔx)



Current

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Number of charges = (n) * (AΔx)

Total amount of charge = (number of charges)*(charge)ΔQ = (n A Δx)*(q)


Number of charges = (charge density or charge per volume)*(volume)


Current

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+ Total volumeV = (A)(Δx)


ΔQ = (n A Δx)*(q)


Current

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length = Δx = vd ΔtArea = A

ΔQ = (n A Δx)*(q)but charges have drift velocity vd = Δx/Δt


Current

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Area = A

ΔQ = (n A vd Δt)*(q)

but charges have drift velocity vd = Δx/Δt

length = Δx = vd Δt

ΔQ = (n A Δx)*(q)


Current

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Area = A

ΔQ/Δt = (n A vd)*(q)

I = n q vd A

but charges have drift velocity vd = Δx/Δt

length = Δx = vd Δt

ΔQ = (n A vd Δt)*(q)

ΔQ = (n A Δx)*(q)


Current

This is the reason why large wires are needed to support large currents


Resistance

Current density (J)current per area


Resistance


Direction of current (flow of positive charges) is same with direction of electric field


Resistance



conductivity


Resistance



conductivity (material property)

resistivity (material property)


Resistance



conductivity

resistivity

Current is proportional to conductivity but inversely proportional to resistivity!


Resistance

Current is proportional to conductivity but inversely proportional to resistivity!


Resistance

Current is proportional to conductivity but inversely proportional to resistivity!Current is proportional to the electric potential(specifically potential difference)


Resistance


Ohm’s LawResistancePotential difference

current


Resistance


Ohm’s Law

a much better form than ΔV = I R

ResistancePotential difference

current


Resistance



current


Increasing ΔV increases IIncreasing R decreases I


Resistance



current


Increasing ΔV increases IIncreasing R decreases I

ΔV = I R Increasing R does not increase ΔVCurrent (I) is increased because ΔV is increased


Resistance


Resistance

Important points:

same with capacitance, resistance does not depend on ΔV and I

Resistance depends on material property resistivity ρ, length of wire l and cross sectional area A

direction of the current I is same as direction of electric field

conventional current is flowing positive (+) charges though in reality electrons flow


Recent Equations

I =∆V

R

R =ρl

A

→J = σ

→E =

→E

ρ

→J =

→I

A

→J = nq

→v dA


Exercise

Rank from lowest to highest amount of current

Derive the equation R = ρL/Afrom V = IR, J = E/ρ = I/A, V = EL


Resistance and Temperature

∆T = T − T0

T0 is usually taken to be 25 °C

ρ = ρ0(1 + α∆T )

R =ρl

A

T ↑ ρ ↑


Power

P =∆U

∆t

P =∆(q∆V )

∆t

P =(∆q)(∆V )

∆t

P =∆q

∆t∆V

P = I∆V


Power

P = I∆V

I =∆V

R

P =V 2

RP = I2R


End of Chapter Exercises

An aluminum wire having a cross-sectional area of 4.00 x 10-6 m2 carries a current of 5.00 A. Find the drift speed of the electrons in the wire. The density of aluminum is 2700 kg/m3. Assume that one conduction electron is supplied by each atom.Molar mass of Al is 27 g/mol.

The electron beam emerging from a certain high-energy electron accelerator has a circular cross section of radius 1.00 mm. (a) The beam current is 8.00 µA. Find the current density in the beam, assuming that it is uniform throughout. (b) The speed of the electrons is so close to the speed of light that their speed can be taken as c = 3.00 x 108 m/s with negligible error. Find the electron density in the beam. (c) How long does it take for Avogadroʼs number of electrons to emerge from the accelerator?

Three wires A, B, C and D are made of the same material but of different lengths and radii. Wire A has length L but has radius R. Wire B has length 2L but with radius ½R. Wire C has length ½L but with radius 2R. Wire D has length ½L but with radius ½R.

Rank with increasing resistance

A 0.900-V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of 0.600 mm2. What is the current in the wire?resistivity of tungsten is 5.6 x 10-8 Ω-m


current

Technology

current count

current convention

charges area

electric potential

qbut charges

volumenumber of charges

xnumber of charges

total volume v