-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) 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

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

av

Q

t

I

Instantaneous Electric Current

IdQ

dt

Direct CurrentDC Provided by

batteries

Alternating Current

AC Provided by power

companies

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.

http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/imgele/micohm.gif

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

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.

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 PotentialLow

Potential

http://media-2.web.britannica.com/eb-media/36/236-004-D4AA985F.gif

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

A Battery Provides EnergyElectric Circuit The battery

“pumps” positive charges from

low (-) to

high (+) potential.

Resistors use up EnergyElectric 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 SpeedIav = 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

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?

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 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 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 metalsR= Ro(1 +α T)

Ro : reference resistance usually at 20oC (sometimes at 0o 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 TC

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 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 = nqvdA /AJ=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

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: 2

lnb

a

ρ bR dR

πL a

2

ρdR dr

πrL

Derivation of Ohm’s Law

b

ba

a

V E ds E

IV J

A

+

+

+

+

+

+

E J

ba

E J

ba

ba

V IA

V IR

RA A

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= the average time interval between successive collisions

vf avg = vd

vd = (qE/me)

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/vav

2

e

nq τσ

m

J = nqvd = (nq2E / me)J=E