Question

A certain wire has a resistance R. What is the resistance of asecond wire, made of the same material, that is half as long and hashalf the diameter?

Answer 1

Given:

Resistance = R

Lenght of second wire (L2)= half of the first wire's lenght (L1) = L1/2

Diameter of the second wire (D2)= Half of the first wire's diameter(D1) = D2/2

Apply:

$R=\frac{\rho L}{A}$

Where:

R= resistance

ρ= resitivity

L= lenght

A = cross sectional area

Replacing:

R = ρL2/A2

R= ρ (L1/2)/ (πd2^2 /4 )

R= 2ρL / π (d/2)^2

R= 2ρL / [πd^2/4]

R=2 ( 4ρL/πd^2)

R= 2R

Answer = 2R