Question

a copper wire has diameter 0.5 mm and resistivity of 1.6 * 10 -⁸ ω m.the length of the wire to make its resistance is​

Answer 1

Given :-

→ Diameter of the copper wire = 0.5 mm

→ Resistivity = 1.6 × 10⁻⁸ Ω m

→ Resistance = 10 Ω

To find :-

→ Length of the wire.

Solution :-

Radius of the wire = Diameter/2

= 0.5/2

= 0.25 mm

= 2.5 × 10⁻⁴ m

Area of cross section of the wire :-

= πr²

= 22/7 × (2.5 × 10⁻⁴)²

= 22/7 × 6.25 × 10⁻⁸

= 19.6 × 10⁻⁸

= 1.96 × 10⁻⁷ m

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Now, we know that :-

R = ρL/A

Substituting values, we get :-

⇒ 10 = [1.6 × 10⁻⁸ × L]/[1.96 × 10⁻⁷]

⇒ 10 = 0.81 × 10⁻¹ × L

⇒ 10 = 0.081L

⇒ L = 10/0.081

⇒ L = 123.45 m

Thus, length of the wire is 123.45 m .