Question

A copper wire has diameter 0.5 mm and resistivity 1.62×10-8 ohm-m .what will be the length of the wire to its resistance 10 ohm ? How much does the resistance change if the diameter is doubled ​

Answer 1

Answer:

Given :

Resistivity ρ = 1.6 × 10⁻⁸ Ω m

Resistance R = 10 Ω

Diameter d = 0.5 mm

= > Radius r = 0.25 mm = 0.25 × 10⁻³ m = 2.5 × 10⁻⁴ m

= > Area A = 6.25 π × 10⁻⁸ m²

We are asked to find length L :

We know :

R = ρ ( L ) / ( A )

= > L = ( R × A ) / ρ

Putting values here we get :

= > L = ( 10 × 6.25 π × 10⁻⁸ ) / 1.6 × 10⁻⁸ m

= > L = 62.5 π / 1.6

= > L = 122.72 m

Hence we get required answer

Answer 2

Answer:

Area of cross-section of the wire, A =pi (d/2) 2 Diameter= 0.5 mm = 0.0005 m Resistance, R = 10Ohm We know that length of the wire = 122.72 m If the diameter of the wire is doubled, new diameter = 2 0.5 = 1mm = 0.001 m Let new resistance be R Therefore, the length of the wire is 122.7 m and the new resistance is 2.5 Ohm.