There are three copper wires of length and cross sectional

There are three copper wires of length and cross sectional area (L, A),[2L,(1/2)A] ,[(1/2)L, 2A] . In which case is the resistance minimum?

1. It is the same in all three cases
2. Wire of cross-sectional area 2A
3. Wire of cross-sectional area A
4. Wire of cross-sectional area 1/2 A

R - ρ	L
	A

R₁ = ρ	L	...(i)
	A

R₂ = ρ	2L	× 2 ...(ii)
	A

R ₃ = ρ	L	=	ρL	...(iii)
	2.2A		4A

⇒ R₃ < R₁ < R₂