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:
[tex]R=\frac{\rho L}{A}[/tex]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
