Chapter 30
Physics II
Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI I
Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html
95.144
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

Up to this point we were talking about electrostatic equilibrium when a conductor was at the same potential and there was no current.
In this case, an electron bounces back and forth between collisions, but its average velocity is zero.
Now if we add a battery, a potential difference will be imposed and the electrons will start travelling creating a current
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

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: current is the rate at which charge flows dQ
The SI unit for current is the coulomb per second, which is called the ampere.
1 ampere = 1 A = 1 C/s.
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

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.
95.144 Danylov Lecture 10
Department of Physics and Applied Physics


ConcepTest 1 Current
Every minute, 120 C of charge flow through this cross section of the wire.
A) 240 A
B) 120 A
The wire’s current is
C) 60 A
D) 2 A
E) Some other value
.

A
The current density J in a wire is the current per square meter of cross section:
The current density has units of A/m 2 .
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

For a junction, the law of conservation of current requires that
I out1
I in
I out2
I in
=I out1
+I out2
I in1
I in2
I out
95.144 Danylov Lecture 10
Department of Physics and Applied Physics
I in1
+I in2
=I out
This basic conservation statement is called
Kirchhoff’s junction law.

ConcepTest 2 Conservation of Current
A) 16 A to   the   right

The current in the fourth wire is
B) 4 A to   the   left
C) 2 A to   the   right
D) 2 A to   the   left
E) Not   enough   information   to   tell
For a junction, the law of conservation of current requires that
Assume I x is out (to the right)
2 A+5 A=9 A+I x
I x
= -2 A
So, the assumption that I x is to the right was wrong.
It is to the left.
I x

95.144 Danylov Lecture 10
Department of Physics and Applied Physics

Consider 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)
If we keep changing ∆ V and measure I and plot it, we will get a straight line.
So ∆ V ~ I
The coefficient of proportionality is called the electrical resistance, R
The SI unit of resistance is the ohm.
1 ohm  1   1 V/A
Ohm’s Law is not a fundamental law but is an experimental relationship that metals obey.
95.144 Danylov Lecture 10
Department of Physics and Applied Physics
∆ V
∆ V

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
Current flows from a positive terminal of a battery to a negative one.
(b) Is the current greater at point A or at point B?
Current
A) A>B
B) B>A
C) A=B

ConcepTest 4 Resistor
Both segments of the wire are made of the same metal. Current I
1 flows into segment 1 from the left. How does current I
1 in segment 1 compare to current I
2 in segment 2?
A) I
1
> I
2
B) I
1
=
I
2
C) I
1
< I
2
D) There’s   not   enough   information   to   compare   them
How   about   current   density   J ?
Since A
1
 A
2 then J
1
 J
2
.

95.144 Danylov Lecture 10
Department of Physics and Applied Physics
Let’s look deeper in Resistance

Consider a cylindrical piece of wire/resistor:
A
ρ – called the
and depends on the material used
We define the resistance R of a long, thin conductor of length L and cross-sectional area A to be:
Units
The reciprocal of the resistivity is called the conductivity
L
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

Resistivity ( ρ ) describes only the material (Au, Co,…).
Resistance (R) characterizes a specific piece of the conductor with a specific geometry
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

95.144 Danylov Lecture 10
Department of Physics and Applied Physics

95.144 Danylov Lecture 10
Department of Physics and Applied Physics

95.144 Danylov Lecture 10
Department of Physics and Applied Physics

ConcepTest 5 Wires I
A.
Two wires, A and B , are made of the
= same metal and have equal length ,
B.
= 2 but the resistance of wire A is four C.
times the resistance of wire B . How do their areas compare?
D. 4 =
E.
2 =
(area)
(area)
L
The resistance of wire A is greater because its area is less than wire B. ratio

Chapter 30 (Knight)
Sections
 30.1
 30.3
 30.4
 30.5
95.144 Danylov Lecture 10
Department of Physics and Applied Physics

95.144 Danylov Lecture 10
Department of Physics and Applied Physics