Question

The specific resistance of a wire is ρ, its volume is 3m3 and its resistance is 3 ohm,what will be its length?

Answer 1

resistance R = ρ L / A , 

       we have Volume V = A L     => A = V / L
 
      ρ = A R / L = V R / L²

     L² = V R / ρ =  3 * 3 / ρ

          L = 3 / √ρ  meters.

Answer 2

Resistance of the wire, R = ρl/a

we know,

volume = AL

=> A = V/L

ρ=  AR/L

=> VR/$L^{2}$

=> $L^{2}$ = VR/ρ

                            = 3× 3/ρ

∴L = 3/√ρ meters.