Question

Two wires A and B are made of copper. The wire A is long and thin while the wire B is short and thick. Which one is correct ?

• A. Both will have same resistivity
• B. Resistivity of A greater than of B.
• C. Resistivity of A less than of B.
• D. none of these.

Answer 1

The correct option is A Both will have same resistivity

Electrical resistivity is an intrinsic property that quantifies how strongly a given material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. Resistivity is commonly represented by the Greek letter $\rho$ (rho). The SI unit of electrical resistivity is the $ohm-meter(\Omega -m)$.
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. Hence, the resistance of a given material will increase with the length, but decrease with increasing cross-sectional area.
In this case, two wires A and B are made of copper and so there would no change due to the material of the wire. The A wire is made thin and long compared to the B wire which is short and thick.
Hence, the wire A has more resistance as the resistance of a given material will increase with the length, but decrease with increasing cross-sectional area.