Question

the resistance of a wire of radius 0.01cm is 10 ohm if the resistivity of the material is 5×10^-7 ohm meter find the length of the wire​

Answer 1

Answer :-

Length of the wire is 0.628 m .

Explanation :-

We have :-

→ Radius of the wire (r) = 0.01 cm = 10⁻⁴ m

→ Resistance (R) = 10 Ω

→ Resistivity (ρ) = 5 × 10⁻⁷ Ωm

________________________________

Firstly, let's calculate the area of cross section of the wire .

⇒ A = πr²

⇒ A = 3.14 × 10⁻⁴ × 10⁻⁴

⇒ A = 3.14 × 10⁻⁴⁻⁴

⇒ A = 3.14 × 10⁻⁸ m²

________________________________

Now, let's calculate the length of the wire .

R = ρl/A

⇒ 10 = (5 × 10⁻⁷ × l)/(3.14 × 10⁻⁸)

⇒ 10 × 3.14 × 10⁻⁸ = 5 × 10⁻⁷ × l

⇒ 3.14 × 10⁻⁷ = 5 × 10⁻⁷ × l

⇒ l = (3.14 × 10⁻⁷)/(5 × 10⁻⁷)

⇒ l = 3.14/5

⇒ l = 0.628 m

Answer 2

Given :-

The resistance of a wire of radius 0.01cm is 10 ohm if the resistivity of the material is 5×10^-7 ohm meter

To Find :-

Length of wire

Solution :-

We know that

Area = πr²

Radius = 0.01 cm = 0.01 = 10⁻⁴ m

Area of circle = πr²

Area = 3.14 × (10⁻⁴)²

Area = 3.14 × 10⁻⁸ m²

Now

ρ = RA/I

5 × 10⁻⁷ = 10 × 3.14 × 10⁻⁸/l

5 × 10⁻⁷ = 3.14 × 10⁻⁷/l

5 × 10⁻⁷/3.14 × 10⁻⁷ = l

5/3.14 = l

5/314 × 100/1 = l

500/314 = l

0.62 = l