# Factors Affecting the Resistance of Wire

**Topics:**Electrical resistance, Area, Electric current

**Pages:**11 (1871 words)

**Published:**March 23, 2005

· Length

· Temperature

· Cross sectional area

· Material

· Magnetism

The factor that we are going to change is the cross sectional area.

Hypothesis: I think that the higher the cross sectional area, the lower the resistance in the conductor will be. This is because the Resistance in a metal conductor happens because as the electrons move through the material (once a voltage has been applied) they collide with the atoms in the material and as a result lose some of their energy. The idea of resistance is simply how difficult it is for the electrons to move through a material. The more difficult it is, the more energy they lose in the material on their travels.

We define electrical resistance as the ratio of voltage to current.

The equation we use to find the resistance from the current and voltage is:

Resistance (R) = Voltage (V) ÷ Current (I)

Put more simply, it is the number of volts difference across the object when one amp of current flows. You should recall that voltage is the number of joules of energy transferred by one coulomb of charge, and that current is the number of coulombs of charge passing a place each second.

What the object is made of will have an effect on its resistance. Not all metals even are equally as good at conducting electricity. A longer length will also make it more difficult for current to flow, as there is more material to travel through.

The temperature of a metallic conductor will also affect the resistance. A hot metal has a larger resistance than a cooler one, but this is tricky to test reliably in the laboratory because the temperature has to be a lot higher to get a decent change in resistance.

Current is nothing but the rate of flow:

But when the temperature rise takes place, the lattice atoms also vibrate in their own equilibrium more vigorously impeding the flow of electric charges due to more frequent collisions.

More electrons are available to conduct the current in the wire. Collisions with lattice ions are less frequent. The Current increases and resistance decreases.

However, the cross-sectional area will also have an effect, as the larger this is, the more charge can travel simultaneously through a given length. Therefore, a larger area of cross-section actually reduces the resistance. It is like having identical lengths sat side by side to be in parallel.

The cross sectional area has a continuous variable, i.e. one that is measured and can have any value. You can put your results onto a point graph and get meaningful conclusions. That is why I have chosen to change the cross sectional area of the conductor.

The main equation that describes the resistive behavior of a piece of uniform metallic wire is R = resistance in ohms

r = resistivity in ohm-metres

l = length in metres

A = area of cross-section in square-metres

The resistivity is simply a constant number for the particular material that makes the numbers work out in S.I. units. The resistivity of Constantan wire is 47× 10 Wm. Different materials have different resistivities; the higher the resistivity the larger the resistance for a given length and cross-section.

We can see from this equation that if the material and area are kept constant, then the equation shows that resistance is directly proportional to the length assuming the wire is uniform. Hence, if you double the length, you double the resistance. As I have said already, it is like having two identical resistors in series.

To verify this you will need to take many values of resistance and length, and then plot resistance against length on a graph. If the graph is a straight line through the origin of the graph then you have verified the equation.

Now, taking cross-section you can either measure the resistance for wire from...

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