Question

A rod, in the form of a cylinder of length L and circular cross-section of radius r, has a resistance R. What is the new value of the resistance R if the length is doubled (2L) and the radius is doubled (2r)?

Answer 1

Solution) Length , L1 = L

L2 = 2L

Radius , r1 = r

r2 = 2r

Resistance , R1 = R

R2 = ?

We have

Resistance , R = ((rho)(L))/(A)

A = (pi)(r^2)

rho is resistivity

So resistance is directly proportional to Length and inversely proportional to square of radius

(R2/R1) = (L2/L1)(r1/r2)^2

(R2/R1) = (2L/L)(r/2r)^2

(R2/R1) = (1/2)

R2 = (R1/2)

R2 = (R/2)