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