L10 Ch30 Current
Transcript of L10 Ch30 Current
Department of Physics and Applied Physics95.144 Danylov Lecture 10
Lecture 10
Chapter 30
Current
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
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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
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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
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ResistanceOhm’s Law
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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
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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
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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