Please answer the following questions and also mention the concepts incolved and why the incorrect options are wrong.
Dear student,
Let R1, L1 and r1 be the initial resistance, length and radius of the wire respectively and R2, L2 and r2 be the final, ρ be the resistivity of the material.
We have
L2 =2L1
r2 = 2r1
R1 = ρL1/A1
=> ρ = R1A1/L1 ---1
R2 = ρL2/A2
=> ρ = R2A2/L2 ---2.
By 1 and 2.
R1A1/L1 = R2A2/L2
A1 = πr1 2
A2 = πr2 2
=> R1 πr1 2/L1 = R2 πr2 2/L2
=> R1 r1 2/L1 = R2 r2 2/L2
=> R1 r1 2/L1 = R2 (2r1) 2/(2L1)
=> R1 = 2 R2
=> R2 = ½ R1
option 3 is correct
The specific resistance of wire is independent of geometry of the wire, it only depends on the material of the wire.
Regards