You have an aluminum bar of dimensions 2cm*5cm*10 cm. You want to put it into electric circuit such a way that this bar will demonstrate the smallest possible resistance. You should connect your bar to the opposite faces with dimensions of:

R = 0.106micro ohms

Explanation:

For a given shape, the resistance depends on the material of which the object is composed. Different materials offer different resistance to the flow of charge. We define the resistivityρ of a substance so that the resistance R of an object is directly proportional to ρ. Resistivity ρ is an intrinsic property of a material, independent of its shape or size. The resistance R of a uniform cylinder of length L, of cross-sectional area A, and made of a material with resistivity ρ, is

R

=

ρ

L

A

The dimension of the Bar is LxBxH

L = 2cm = 0.02m, B = 5cm = 0.05m, H = 10cm = 0.10m.

the Area, A = BxH = 0.05 x 0.1 = 0.005m2.

the resistivity of Aluminum, p = 2.65x10-8

the resistance of the aluminum is

R = p xL/A = 2.65x10-8 x 0.02/0.005

= 0.000000106ohms

= 0.106micro ohms