Question

what happens to the resistance of a conductor when the lenght is reduced to half ?

Answer 1

R1 = Resistance before reduction of length
R2 = Resistance after reduction of length
L = Length of conductor
A = Area of cross section of conductor
P = Resistivity

now,
R1 = PL/A
and,
R2 = (P×(L/2))/A
=> R2 = PL/2A

now R1 / R2 = (PL/A)/(PL/2A)
=> R1/R2 = (PL/A) × (2A/PL)
=> R1/R2 = (PL × 2A)/(PL × A)
=> R1/R2 = 2
=> R2 = R1/2

therefore the resistance when the length is reduced will be half of the original resistance before the reduction of length