Can you tell me how to solve this problem?(based on circuits)?

Question

a copper wire of a.162 cm diameter with resistance 0.4 ohm. when the diameter is reduced to 0.032 cm what will be the resistance?

(the specific resistance and the total value remains constant)

Answer 1

The one fact: resistance of a wire is inversely proportional to the cross-sectional area.  (and of course, area is proportional to linear dimension squared).

You are reducing the diameter by a factor of 32/162 or 0.197

This means the area is being reduced by that factor squared or 0.039

Which means the resistance will be increased by 1 over that or 25.6

therefor R is 25.6 x 0.4 or 10.3 ohms

PS, your comment "specific resistance and the total value remains constant" is meaningless. The resistance increases, as does the total resistance. I think you mean resistivity remains constant.

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Answer 2

If the diameter is reduced by a factor of, say 2, the area will be reduced by 2^2. Since the resistance is inversely proportional to the area, in this case it would be reduced by a factor of 1/4.

You should be able to see that.

In the specific case, the diameter is reduced by a factor of 5.0625, so the resistivity, and thus the total resistance, would be reduced by a factor of 1/25.629, which would be 3.9 percent.