Investigating Resistance– To investigate if and how a wires length affects the resistance.

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Investigating Resistance – To investigate if and how a wires length affects the resistance.

Problem:

Altering the number of cells or the voltage supplied from the power pack can change the amount of current flowing through a wire. However, the amount of current will also depend upon the resistance of the wire. The resistance, in turn, depends upon certain characteristics of the wire itself.

Task / Aim:

To investigate if and how a wires length affects the resistance.

Theories & Formulae:

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made. Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as

The factor in the resistance which takes into account the nature of the material is the resistivity. Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry.

Resistance

Whether or not a material obeys Ohm's law, its resistance can be described in terms of its bulk resistivity. The resistivity, and thus the resistance, is temperature dependent. Over sizable ranges of temperature, this temperature dependence can be predicted from a temperature coefficient of resistance.

Ohm's Law

For many conductors of electricity, the electric current which will flow through them is directly proportional to the voltage applied to them. When a microscopic view of Ohm's law is taken, it is found to depend upon the fact that the drift velocity of charges through the material is proportional to the electric field in the conductor. The ratio of voltage to current is called the resistance, and if the ratio is constant over a wide range of voltages, the material is said to be an "ohmic" material. If the material can be characterized by such a resistance, then the current can be predicted from the relationship:

ADVANCED RESEARCH:

Microscopic View of Ohm's Law

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The current density (electric current per unit area, J=I/A) can be expressed as

The number of free electrons, assuming one per atom, is

From the standard form of Ohm's law and resistance in terms of resistivity:

The next step is to relate the drift velocity to the electron speed, which can be approximated by the Fermi speed:

The drift speed can be expressed in terms of the accelerating electric field E, the electron mass, and the characteristic time between collisions.

The conductivity of the material can be expressed in terms of the Fermi speed and the ...

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