Question

A copper wire has diameter 1 mm and resistivity of 1.5 x 10-8 m. What will be the length of this wire to make its resistance 5 2? How much does the resistance change if the diameter is half?​

Answer 1

We have,

• Diameter of wire = 1mm = 1 × 10-³ m , Radius = 10-³/2
• Resistivity of conductor = 1.5 × 10-⁸ m
• Resistance of wire = 5 Ω

Now we know that, the formula for resistance is;

• R = ρ L/A

= R = ρ L/A

= 5 = 1.5 × 10-⁸ × L /πr²

= 5 × 10⁹/15 = L /3.14 × 10-³/2

= 10⁹/3 = L /1.57× 10-³

= 10⁹ × 157 × 10-² × 10-³/3

= 10⁹ × 157 × 10-⁵/3

= 52.3 × 10⁴ m

Therefore, the length of the conductor is 52.3 × 10⁴ m.

Now,if the diameter will be halfed then;

• R = ρ L/A
• R = 1.5 × 10-⁸ ×52.3 × 10⁴ /1.57× 10-³
• R = 2.49

As, the length is reduced to half, thus the resistance will also be halfed.

__________________________

Thank youu!! :)) $\;$