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)?
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)
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