A wire of length L,diameter d,resistance R is made of material with resistivity $\rho$.If I take the wire and cut it into five equal pieces and then put those pieces in parallel to make one single thick wire L/5 in length,what will be its resistance?

Question

Quizplus · Accepted Answer

The resistance of a wire is directly proportional to its length and resistivity, and inversely proportional to its cross-sectional area.

When we cut the wire into five equal pieces, the length of each piece becomes L/5, and the cross-sectional area becomes ((d/2)^2)π/5 (since we have 5 pieces in parallel of the same length and diameter).

Therefore, the resistance of each piece becomes R/5 (since ρ is constant).

When we connect them in parallel, the overall resistance of the wire becomes:
1/(1/5 * R/5) = 5R/25 = R/5

So the answer is (B) R/25.

A Wire of Length L,diameter D,resistance R Is Made of Material