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PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Lecture 12
Chapter 27
Current
Physics II
I like current measurements
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
Electric current islike current of runners
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Today we are going to discuss:
Chapter 27:
Section 27.1 Section 27.3-5
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
A Model of Conduction
Up to this point we were talking about electrostatic equilibrium when a conductor was at the same potential and there was no current.
Now if we add a battery, a potential difference will be imposed and the electrons will start travelling creating a current
In this case, an electron bounces back and forth between collisions, but its average velocity is zero.
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Current (definition)
IfQisthetotalamountofchargethathasmovedpastapointinawire,wedefinethecurrentIinthewiretobetherateofchargeflow:
The SI unit for current is the coulomb per second, which is called the ampere.
1 ampere = 1 A = 1 C/s.
currentistherateatwhichchargeflows
dQ
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Direction of current (convention)
By convention, current is defined as flowing of motion positive particles from + to -.
Electrons actually flow in the opposite direction.
Current (by convention motion of positive particles)
Current
Current flows from a positive terminal of a battery to a negative one.
Current (by convention motion of positive particles)
Every minute, 120 C of charge flow through this cross section of the wire.
A) 240 A
B) 120 A
C) 60 A
D) 2 A
E) Some other value
ConcepTest Current
The wire’s current is
𝐼𝑑𝑄𝑑𝑡
120 𝐶60 𝑠𝑒𝑐 2 A
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
The Current Density in a Wire
The current density J in a wire is the current per square meter of cross section:
The current density has units of A/m2.
AdQ
Density!? Again!?
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Conservation of Current
Forajunction, the law of conservation of current requires that
Iin =Iout1+Iout2Iin
Iout1
Iout2
This basic conservation statement is called Kirchhoff’s junction law.
Withoutajunctionpoint,the law of conservation of current :
The current in the fourth wire is
A)16 A to the right
B)4 A to the left
C)2 A to the right
D)2 A to the left
E)Not enough information to tell
ConcepTest Conservation of Current
Forajunction,thelawofconservationofcurrentrequiresthat
So,theassumptionthatIxistotherightwaswrong.Itistotheleft.
AssumeIxisout(totheright) Ix
2 A+5 A=9 A+Ix
Ix= -2 A
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
ResistanceOhm’s Law
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Ohm’s Law
Consider a piece of wire. For a current to exist, there must be a potentialdifference between its ends (just as a difference in height betweensource and outlet is necessary for a river current to exist)
The coefficient of proportionality is called the electrical resistance, R
𝑂ℎ𝑚 𝑠 𝑙𝑎𝑤
The SI unit of resistance is the ohm.1 ohm 1 1 V/A
∆V
If we keep increasing ∆V across a resistor, I will keep increasing as well.But if you look at their ratio, you will be surprised to see that it isalways a constant. That constant looks like an intrinsic property of theresistor. Let’s give it a nice name – the electrical RESISTANCE, R.
Ohm’s Law is not a fundamental law but is an experimental relationship that metals obey.
Who is Ohm? It’s my show!
𝑅 ≝Δ𝑉𝐼
Lier!!!
∆V
I
ConcepTest Resistor
Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B?
A)A>B
B) B>A
C) A=B
(b) Is the current greater at point A or at point B?A)A>B
B) B>A
C) A=B
CurrentCurrent flows from a positive terminal of a battery
to a negative one.
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Ohm’s Law
Let’slookdeeperintheResistance
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Resistivity
L
A 𝑅 𝜌𝐿𝐴
Acceleration
ACCR Collision
“The train of action” of an electron moving through a crystalline structure
ConcussionRecovery
Thus, the longer a resistor, the larger number of collision of an electron and the larger the resistance, R
𝑹~𝑳
A is small, Resistance is large
A is large, Resistance is small
𝑹~𝟏/𝑨
𝐴𝑙𝑢𝑚𝑖𝑛𝑢𝑚 𝐺𝑜𝑙𝑑
They obviously should have different resistance. To describe that, the
resistivity was introduced.
ρ – called the resistivity and depends on the material used
𝑹~ρ
The resistance, R, depends on material and a geometry of the element.
(We saw something similar when we introduce capacitance of a parallel-plate capacitor).
𝐶 𝜀𝐴𝑑
We define the resistance R of a long, thin conductor of length L and cross-sectional area A to be:
ρ ΩmUnits
The reciprocal of the resistivity is called the conductivity 𝜎1𝜌
Imaginarysituationofhugedoors
Realsituationofsmalldoors
End of class
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Resistance –vs- Resistivity
Resistivity(ρ) describes only the material (Au, Co,…).
Resistance(R) characterizes a specific piece of the conductor with a specific geometry
𝑅 𝜌𝐿𝐴
ConcepTest Resistor
Both segments of the wire are made ofthe same metal. Current I1 flows intosegment 1 from the left. How doescurrent I1 in segment 1 compare tocurrent I2 in segment 2?
A) I1 > I2B) I1 = I2
C) I1 < I2D) There’snotenough
informationtocomparethem
How about current density J? J1 J2.Since A1 A2 then
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Example Current
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Example Resistance
PHYS.1440 Lecture 12 A.DanylovDepartment of Physics and Applied Physics
Thank you
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