Question

The resistance of a wire is 0.01 cm radius is 10 ohm. If the resistivity of the material of wire 50*10 to the power -8 ohm meter,find the length of the wire.

Answer 1

resistance of wire , R = 10 ohm
radius of base of wire , r = 0.01cm = 0.01/100 m
r = 1 × 10^-4 m
base area , A = πr² = 3.14 × (10^-4)² = 3.14 × 10^-8 m²
resistivity of the material of wire , ρ = 50 × 10^-8 ohm.meter

we know, formula
R = ρL/A
L = RA/ρ
= 10 ohm × 3.14× 10^-8m²/50 × 10^-8 ohm.meter
= 31.4/50 m
= 0.628 m


hence, length of wire is 0.628 m

Answer 2

Answer:

Explanation:

Question :-

The resistance of a wire of 0.01 cm radius is 10 Ω. If the resistivity of the material of the wire is 50 × 10⁻⁸  ohm meter, find the length of the wire.

Given :-

Radius = 0.01 cm = 0.01 × 10⁻² m

Resistivity, ρ = 50 × 10⁻⁸ Ωm

Resistance R = 10 Ω

Solution :-

⇒ R = ρ × l/A

⇒ R = ρ × l/πr²

⇒ l = Rπr²/ρ

⇒ l = 10 × 3.14 × 0.01 × 10⁻² × 0.01 × 10⁻²/50 × 10⁻⁸

⇒ l = 314 × 10⁻⁴/50 × 10⁻⁸ × 10⁵

⇒ l = 6.28 × 10⁻⁴/10⁻³

⇒ l = 0.628 m.

Hence, the length of the wire is 0.628 m.