Department of Physics and Applied Physics95.144 Danylov Lecture 10

Lecture 10

Chapter 30

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Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html

Physics II

95.144

Department of Physics and Applied Physics95.144 Danylov Lecture 10

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.

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Current (definition)

If Q is the total amount of charge that has moved past a point in a wire, we define the current I in the wire to be the rate of charge flow:

The SI unit for current is the coulomb per second, which is called the ampere.

1 ampere = 1 A = 1 C/s.

current is the rate at which charge flows

dQ

Department of Physics and Applied Physics95.144 Danylov Lecture 10

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.

.

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 1 Current

The wire’s current is

Department of Physics and Applied Physics95.144 Danylov Lecture 10

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.

A

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Conservation of Current

For a junction, the law of conservation of current requires that

Iin=Iout1+Iout2Iin

Iout1

Iout2

Iin1+Iin2=Iout

Iin1

Iin2 IoutThis basic conservation statement is called

Kirchhoff’s junction law.

The current in the fourth wire isA) 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 2 Conservation of Current

For a junction, the law of conservation of current requires that

So, the assumption that Ix is to the right was wrong. It is to the left.

Assume Ix is out (to the right)Ix2 A+5 A=9 A+Ix

Ix= -2 A

Department of Physics and Applied Physics95.144 Danylov Lecture 10

ResistanceOhm’s Law

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Ohm’s LawConsider a piece of wire. For a current to exist, there must be a potential difference between its ends (just as a difference in height between source and outlet is necessary for a river current to exist)

So ∆V ~ IThe coefficient of proportionality is called the electrical resistance, R

The SI unit of resistance is the ohm.1 ohm 1 1 V/A

∆V

∆V

If we keep changing ∆V and measure I and plot it, we will get a straight line.

Ohm’s Law is not a fundamental law but is an experimental relationship that metals obey.

ConcepTest 3 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.

ConcepTest 4 ResistorBoth segments of the wire are made of the same metal. Current I1 flows into segment 1 from the left. How does current I1 in segment 1 compare to current I2 in segment 2?

A) I1 > I2

B) I1 = I2

C) I1 < I2

D) There’s not enough 

information to compare them

How about current density J? J1 J2.Since A1 A2 then

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Ohm’s Law

Let’s look deeper in Resistance

Department of Physics and Applied Physics95.144 Danylov Lecture 10

ResistivityConsider a cylindrical piece of wire/resistor:

L

A

We define the resistance R of a long, thin conductor of length L and cross-sectional area A to be:

ρ – called the resistivity and depends on the material used

Units

The reciprocal of the resistivity is called the conductivity

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Resistance –vs- ResistivityResistivity (ρ) describes only the material (Au, Co,…).

Resistance (R) characterizes a specific piece of the conductor with a specific geometry

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Problem 14

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Example

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Example (cont.)

The resistance of wire A is greater because its area is less than wire B.

ConcepTest 5 Wires ITwo wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their areas compare?

A. =

B. = 2

C.

D. 4 =

E. 2 =

L

(area)

(area)

ratio

Department of Physics and Applied Physics95.144 Danylov Lecture 10

What you should read

Chapter 30 (Knight)

Sections 30.1 30.3 30.4 30.5

Department of Physics and Applied Physics95.144 Danylov Lecture 10

Thank youSee you on Friday