Question

A piece of wire having resistance R is cut into four equal parts
1) What is the resistance of each part?
2)What is the resistance of their parallel combination?
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Answer 1

Answer:

The expression for resistance of a wire is given by R=p*l/A where p(rho) is called the resistivity of the element that is used to make the wire; l is the length of the wire and A is the area of cross section of the wire.

Since, in this question, the wire is cut into 4 equal parts, that is, the length of each part is now 1/4 th of the original length (=l/4); with the resistivity and A being still the same as there is no change in the material of the wire as well as the area of cross section of the wire.

Therefore, using the above mentioned resistance expression, we can conclude that the resistivity of each of the four cut parts is simply R/4, that is, 0.25% of the original resistance.

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