Question

A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10−8 Ω m. What will be the length of this wire to make its resistance 12 Ω?

Answer 1

Answer:

6.0*10^4 for 12 resistance

Answer 2

Solution :-

• Diameter of the copper wire(d) = 0.5 mm = 0.5 x 10-³ m

• Radius of the copper wire (r)= 0.5 x 10³ /2 = 0.25 x 10-³ m

• Resistance of the wire (R) = 12 Ω

• Resistivity of the wire ( ρ) = 1.6 x 10-⁸ Ω m

Area of cross section (A) = π r² = 3.14 x 0.0625 x10-⁶  = 0.196  x 10-⁶ m²

The resistance of the wire can be given by ,

⟹ R = ρ L / A

On rearranging ,

⟹ L = RA / ρ

⟹ L = 12 x 0.196 x10-⁶ / 1.6 x 10-⁸

⟹ L = 2352 x 10² / 1.6  

⟹ L = 1.47

⟹ L = 147 m

The length of the wire will be 147 m