Question

a nichrome wire has a resistance of 6 ohm. what will be the resistence of another made of the same material having length 3 times and area 2 times that of the first wire

Answer 1

for nichrome wire :

R₁ = resistance = 6 ohm

ρ = resistivity

L₁ = length

A₁ = area

resistance is given as

R₁ = ρL₁/A₁                    eq-1

for other wire :

R₂ = resistance = 6 ohm

ρ = resistivity

L₂ = length = 3L₁

A₂ = area = 2A₁

resistance is given as

R₂ = ρL₂/A₂                  

R₂ = ρ (3L₁)/(2A₁)

R₂ = (1.5) (ρL₁/A₁ )

using eq-1

R₂ = (1.5) R₁

R₂ = (1.5) (6)

R₂ = 9 ohm