A conducting wire has a resistivity

[Jay9313]

Homework Statement

A conducting wire has a resistivity, ρ as a function of its length, L, given by ρ=(ρ0)(L) where (ρ0) is constant. A is the cross-sectional area of the wire. the resistance of the wire would be
A) [(ρ0)(L)]/A
B) (ρ0)/(2A)
C) [(ρ0)(L)]/(2A)
D) [2(ρ0)(L^2)]/A
E) [(ρ0)(L^2)]/(2A)

Homework Equations

r=(ρL)/A

The Attempt at a Solution

r=[(ρ0)(L^2)]/A

Am I missing something?

 

[SammyS]

Homework Statement

A conducting wire has a resistivity, ρ as a function of its length, L, given by ρ=(ρ0)(L) where (ρ0) is constant. A is the cross-sectional area of the wire. the resistance of the wire would be
A) [(ρ0)(L)]/A
B) (ρ0)/(2A)
C) [(ρ0)(L)]/(2A)
D) [2(ρ0)(L^2)]/A
E) [(ρ0)(L^2)]/(2A)

Homework Equations

r=(ρL)/A

The Attempt at a Solution

r=[(ρ0)(L^2)]/A

Am I missing something?

Yes.

For a (very short) length, ΔL, of wire, the resistance, ΔR is given by, $\displaystyle \Delta R=\rho\frac{\Delta L}{A}=\left(\rho_0 \cdot L\right)\frac{\Delta L}{A}\,.$