Question

A copper wire has diameter 0.5 mm and resistivity of 1.6 x 10−8 Ω m. What

should be the lenght of this wire to make its resistance 10 Ω.​

Answer 1

Answer:

122.72 m

Explanation:

Resistivity (ρ) = 1.6 × 10-8 Ω m

Resistance (R) = 10 Ω

Diameter (d) = 0.5 mm

d = 5 × 10⁻⁴ m

Hence, we will get radius

Radius (r) = 0.25 mm

r = 0.25 × 10⁻³ m

r = 2.5 × 10⁻⁴ m

We need to find the area of cross-section

A = πr2

= (22/7)(2.5 × 10⁻⁴)2

= (22/7)(6.25×10⁻⁸)

= 1.964 × 10-7 m2

We have to find the length of the wire

Let the length of the wire be L

We know that

R = ρ (L) / (A)

L = (R × A) / ρ

Substituting the values in the above equation we get,

→ L = (10 × 1.964 × 10⁻⁷) / 1.6 × 10⁻⁸ m

→ L = 1.964×10-6 /1.6 × 10-8

→ L = 122.72 m

Therefore the length should be 122.72 m

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