-electric current -resistance -factors that affect resistance -microscopic view of current ap...
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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
av
Q
t
I
Instantaneous Electric Current
IdQ
dt
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Direct CurrentDC Provided by
batteries
Alternating Current
AC 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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http://hyperphysics.phy-astr.gsu.edu/HBASE/electric/imgele/micohm.gif
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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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
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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.
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A Battery Provides EnergyElectric Circuit The battery
“pumps” positive charges from
low (-) to
high (+) potential.
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Resistors use up EnergyElectric Circuit
When the current goes through the resistor it goes to a lower potential.
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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 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
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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
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 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)
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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
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Semiconductors = 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 /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
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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: 2
lnb
a
ρ bR dR
πL a
2
ρdR dr
πrL
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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
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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= the average time interval between successive collisions
vf avg = vd
vd = (qE/me)
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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