Download Current, Resistance, and Electromotive Force

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Electric Current
Electric Current is defined as the movement of charge from one
region of space to another, and is denoted by a capital I.
Current, Resistance, and
Electromotive Force
In conductors electrons move around freely, but since they are
going off in all different directions the net current in any normal
piece of metal such as copper would be zero. However if an
electric field were passed through the copper wire the free
charges would begin to move in one specific direction resulting
in a current.
©2011 by Bryan Pflueger
The motion of these particles is referred to as the drift velocity
(vd).
The electrons constantly collide with the ions fixed within the
conductor's structure and this results in vibrations which begin
to generate heat and slow the particles motion from a magnitude
of 106 m/s to 10-4 m/s.
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Electric Current
Electric Current
+
+
+
_
_
+
+
_
Before Electric Field
+
+
_
+
+
_
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_
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Both positive and negative charges can generate an electric
current, but only when they pass through certain materials.
In metals only electrons can flow, but in ionized gases, such
as plasma, both electrons and positive ions are able to flow.
+
After Electric Field
Once the electric field is turned on their is a net force to the
right on the positively charged particles, and a net force to the
left on the negative particles. The negative charges would
actually move, but the sign of the charge has no effect on
solving problems dealing with circuits. So for the purpose of
remaining conventional we always say that current flows in
the direction of the positive charges, this is referred to as the
conventional current.
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Electric Current
Electric Current
+
+
+
+
+
When a current is passing through a wire we state that the
current is in the direction the positive charges are moving.
In the diagram above the positive charges are flowing
through a specific area in a certain amount of time. This is
what we define current as, the rate at which the charge flows
through the wire.
The units for current is a Coulomb/second, better known
as the ampere.
A
+
+
+
Lets return to the situation we just talked about on the last slide.
A current is flowing through a wire and we want to find the rate
at which the charges are flowing through a cross sectional area
of A. The distance each charge moves can be represented as vd
dt. If we now multiply by A we find the volume that the charges
flow through in the given time. Then multiply by the
concentration of the charge flowing through and the magnitude
of each, this equals the change in charge with respect to time.
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Electric Current
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1
12 C of charge passes a location in a circuit in 10
seconds. What is the current flowing past the
point?
The charge per unit of area is called the current Density, which is
represented by a J.
1.2 A
In the general expression for current and current density the
charge q is replaced by its absolute value to show that the
charge does not matter, and the current density can also be
represented in vector form.
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2
How long will it take for 400 C of electric charge to
pass through a copper wire if the current through
it is 1.5 A?
266.67 s
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Resistivity and Resistance
When a current is passing through a wire there is some
resistance to the motion of the charges. The resistivity,
represented as ρ, of a certain material is the ratio of the electric
field to the charge density.
Resistivity is also effected by the temperature it is held at. At
higher temperatures resistivity in a metal conductor increases
because as the material heats up, the particles within it begin to
vibrate more and as a result the moving charged particles will
collide more frequently with the ions increasing the drift velocity,
which increases the current density.
This equation describes that the effect of temperature on the
resistivity is not perfect because it only works up to about 100 oC
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Resistivity and Resistance
Superconductors behave similarly to the change in
temperature as does a metal conductor but at some point
with decreasing temperature it drops off to zero.
Semiconductors behave in the opposite manner as metal
conductors. As the temperature increases the resistivity
decreases, but as the temperature decreases the resistivity
increases.
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Resistivity and Resistance
Since Resistance is directly proportional to Resistivity it
makes sense that Resistance is also affected by the
temperature.
Resistance of Hollow Cylinder
If we allowed a current to flow from the inside of a hollow
cylinder of length L to the outside, we can find the
Resistance by cutting up the radius and adding each of the
pieces of the resistance we find.
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Ohm's Law and Resistance
3
What is the resistance of a copper wire with a length
of 2m, a radius of 5cm, and a resistivity of 2.44x10-8.
A 3.2x10-10 Ω
B 1.8x10-10 Ω
C 2.6x10-9 Ω
D 3.8x10-10 Ω
This shows the relationship between current, voltage, and
resistance, as well as an equation for the resistance.
Ohm's Law
E
4.2x10-9 Ω
Its unit is the Ohm (Ω)
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4
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What is the resistance of a Gold wire of length .5m,
a diameter of 6 cm, and a resistivity of 2.75x10-8.
What is the resistance of a rheostat coil, if 0.05 A
of current flows through it when 6 V is applied
across it?
A 1200 Ω
A 1x10-4 Ω
B 120 Ω
B 1.5x10-5 Ω
C 12 Ω
C 2x10-5 Ω
D
5
D 1.2 Ω
3x10-5 Ω
E 3.5x10-5 Ω
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Electromotive Force
Electromotive Force
If you were to pass an electric field through a conductor
initially there would be a current, but enough charge will build
up quickly on the opposite ends of the conductor producing
an electric field equal in magnitude, but in the opposite
direction, effectively canceling out the current. In order to
maintain a steady current we have to remember that when a
charge moves through a conductor and returns to its starting
point it has last some of its potential energy. To solve this
problem we have to find some device that can increase the
potential energy, such as a battery.
E
I
-E = 0; J = 0
+
+
+
+
All circuits require some source of EMF to increase the potential
energy of the circuit. A battery has two terminals, one positively
charged and the other is negatively charged. When a charge of +q
moves into the battery it experiences two forces, an electrical force
which is due to the electric field present between the two plates
and a non-electrical force, Fn. The non-electrical force could come
from different sources such as, a magnetic field present in a
generator, a chemical reaction in a battery, or a mechanical input.
This prevents the charge from just flowing in a battery, that is why
it holds its potential for a while. If this force did not exist then you
could not create a battery.
E
+
+
+
Fn
+
FE
-
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Internal Resistance
Circuit Components
We sometimes talk about complicated situations in mechanics
when we must account for friction, for example if a string does not
have a negligible mass. In circuits we sometimes have to take into
account the resistance the current will encounter when flowing
into the battery, which effects both the current and the emf of the
battery. In an ideal situation the emf of the battery would be equal
to its potential difference.
Conducting Wire
Resistor
Battery (Source of emf)
If we setup a simple circuit, a battery with an internal resistance r
which is connected to a light bulb of resistance R, Ohm's law
would be written as:
I
and
Battery (Source of emf with a
internal resistance)
R
r
I
A
Ammeter
V
Voltmeter
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6
A 6V battery, whose internal resistance 1.5 Ω is
connected in series to a light bulb with a resistance
of 6.8 Ω. What is the current in the circuit?
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7
A 6V battery, whose internal resistance 1.5 Ω is
connected in series to a light bulb with a resistance
of 6.8 Ω. What is the terminal voltage of the
battery?
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Electrical Energy and Power
We have discussed the potential of the battery, resistance, and
the current it produces, but in electrical systems we are also
concerned with what is the rate at which energy is put into the
system or taken from the system. This quantity is termed power
and is denoted by P.
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Electrical Energy and Power
Power Output
A battery has an internal resistance of r and an emf of
.
and
(Change in charge with respect to time)
(Work done by the battery)
Power Input
If a battery with an emf of is connected to a larger power
source and their currents are flowing in opposite directions,
then the smaller battery will begin gaining energy.
(Power Equations)
(Units of Power)
and
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8
A toy car's electric motor has a resistance of 17 Ω ;
find the power delivered to it by a 6-V battery.
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9
How much voltage must be applied across a 450 Ω
resistor in order for it to consume 120 W of power?