if the volume of the conductor becomes thrice and the length of the conductor becomes 4 times the original, then find the change in the resistance.
pls help NUMERICAL
L - Length, A - Area, V - Volume, ρ - Resistivity, R - Resistance.
Suffix i and j refer to initial and final values.
Final length = 4 times the original.
Lf = 4 Li
Final volume = Thrice intial volume.
Vf = 3Vi
Volume = Area x Length
AfLf = 3AiLi
Af = 3Ai/4
Rf = ρLf/Af = ρ4Li/(3Ai/4) = 16ρLi/3Ai = 16Ri/3
The resistance will be 16/3 times intial resistance.