Download Ohm`s Law and resistance

Ohm’s Law and resistance
So far, we have studying static electric charge, only touching on flow of charge
as it affects the distribution of charge on perfect conductors. It is now time to
begin our study of the flow of electric charge.
The flow of charge is called the current, I, and is measured in units called
amperes or amps (A). The ampere is actually defined in terms of the force
between two current carrying wires, as we will investigate next term. The
Coulomb is defined in terms of the ampere as
1A = 1C/s
When a current flows through a real conductor, there is some resistance to the
flow of charge. To overcome this resistance, a potential difference or voltage
needs to be applied. This is just like fluid flow or heat flow, with the following
correspondences:
Electricity
Potential V
Current I
Resistance R
Fluid
Heat
Pressure P
Temperature difference, ΔT
flow, mass/sec.
heat, Q
valve or clog in pipe 1/conductivity
To measure the resistance quantitatively, it can be related to the potential and
the current as
V = IR
Ohm’s Law
The resistance is the ratio of the potential to the current, R = V/I.
Devices called resistors can be purchased and are an important component in
constructing electronic circuits and products. The resistance of such a resistor
can be related to its construction, just like we did with capacitors. Typical
resistors are made of graphite and often are cylindrical in shape. So how does
the resistance depend on the length, L, and cross sectional area, A, of the
resistor? And, how does the resistance depend on the material if we use
something other than graphite?
Let’s see if we can make some predictions first, then we can check them by
experiment.
Area, A : Think of connecting two or more identical pipes side-by-side or double
the area for heat flowing through a material. How will the fluid flow compare to
that through a single pipe or the heat flow through twice the area compare to the
heat flow through the original area?
Apply your answer to current in electrical resistors and then use Ohm’s Law
above to find the total resistance.
Length, L : As the length of the resistive material in the resistor increases, it’s
resistance changes. Think of two pipes clogged with gravel end-to-end in a
water line or twice the thickness of thermally insulating material. What do you
think the flow through the combination would be compared to the flow through
one of them?
What does this say about the resistance?
Putting all these results together for electrical resistors gives
R  L/A
The resistance also depends on the material the resistor is made from. If we
think of the cylinder of graphite or a metal wire, we can divide out the geometric
factors to leave the material property contributing to resistance:
RA/L =  the resistivity of the material.
The resistivity is a property of the material, like its density and dielectric constant
are. It does not depend on the shape or size of the object.
We now have an expression for the resistance of a resistor in terms of its
construction:
R=  L/A
This also gives us an approach to determining the total resistance for two
resistors in parallel or in series.
Two resistors in series are wired one after the other. This is like increasing the
length of resistive material. Since resistance is proportional to length,
Rtot = R1 + R2 (series)
Two resistors wired in parallel provide two paths for the current, increasing the
total current flow. The total resistance for the two is then less than either of the
resistors alone. This arrangement is like combining areas. Since resistance is
inversely proportional to the area, we get
1/Rtot = 1/R1 + 1/R2 (parallel)
As for the cause of resistance in metals, the electrons are not perfectly free to
move. There are those positively
charged nuclei in the way which tend
to pull them this way and that and
the inner electrons in the metal
atoms which do the same. An
electron moving through a wire is a
bit like a pinball game, with it
bouncing off many obstructions in
random directions and with changing
velocity.
In fact, electrons move quite slowly through even the best conductor: a couple of
centimeters per second. So how does an electric current get to the light bulb so
quickly? This is due to a cooperative movement of electrons. As one electron
moves into a wire at one end, electrons all along the wire move away from that
end and an electron at the other end leaves the wire, all in a very short time.
It’s like a popular concert where the management looks at the flow of people
through the gate which may be dozens of people per second, but you look at it as
taking you half an hour to get to the gate and in.
Now for the next conceptual question. With this picture in mind, what is the
difference in electric charge in a wire with no current flowing versus one carrying
an electric current?