Relationship between the Resistance and Dimensions of a Conductor

With a uniform wire/conductor of a given material and a given length, the resistance obtained by dividing Potential difference between any 2 points by Current is directly proportional to the distance between them. That is to say if the distance between the 2 points (on the conductor) increases the resistance also increases.

If 2 resistors each having resistance R ohms are connected in parallel the equivalent resistance Re is given by Product / Sum (Product over Sum)

Re = R*R/R+R
Re = R*R/2R
Re = R/2
Re = (1/2)*R
Each resistor will offer half of its resistance.

See the working in the slide. Click the previous button then after click on the slide screen.

Therefore, if two wires of the same material, having the same length and diameter are connected in parallel their resistance is half that of one wire. The effect of connecting two wires in parallel is similar to doubling the area of conductor. Connecting 7 wires in parallel is the same as increasing the cross section area of a wire 7 times and this reduces the resistance to a 1/7 (seventh) of one wire. Generally, the resistance of a given length of a conductor is inversely proportional to the cross section area. 


Other factors that influence resistance are; nature of the material (different materials have different resistances) and temperature (the resistance of some materials increase with an increase in temperature). So everything we have discussed above is true if temperature is constant.

Resistance of a wire = (Length of wire (L)/Cross Sectional Area (A))*a constant for a given material (ρ)

See the equation in the slide.

The constant of a material is called Resistivity of a material and it is represented by a Greek symbol rho (ρ). Resistivity is measured in ohm meter (Ωm)

Definition for Resistivity

This is the resistance of the specimen having one meter long and one meter square of cross sectional area.