A metal rod of length 10 cm and a rectangular cross-section of 1cm × 1/2 cm is connected to a battery across opposite faces. The resistance will be

Question

Philoid · Accepted Answer

Here we need to calculate resistance across each connection. For a wire, the resistance(R) is given by

where, ρ is the resistivity of the material, l is the length of the material and A is the area of cross-section.

As ρ is same for the materially A and l change.

For the first case, A=1cm x 0.5 cm = 0.5 cm² and length is 10 cm.

For the second case, A= 10cm x 1 cm = 10 cm² and length is 0.5 cm

And for the third case, A=10 cm x 0.5cm = 5 cm² and the length is 1cm

Therefore, the resistance is maximum in the first case i.e. when the battery is connected across image2.pdf faces.