Question

a wire 150cm long and diameter 1mm is made of an alloy of resistivity 44 into ten to the power minus 8 ohm-meter what is the resistance of the wire

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Answer 1

Copied from @Answering0

Answer:

Resistance of the wire is 451 × 10⁻¹² Ω.

Explanation:

Given that:

A wire 150 cm long and diameter 14 mm is made of an alloy of resistivity  44 × 10⁻⁸ Ω m.

To Find:

What is the resistance of the wire?

Finding the length of wire in meters:

100 cm = 1 m

150 cm = 150/100 = 15 × 10⁻² m

∴ Length of wire = 15 × 10⁻² m

Finding the diameter of the wire in meter:

1000 mm = 1 m

14 mm = 14/1000 = 14 × 10⁻³ m

Diameter = 14 × 10⁻³ m

∴ Radius = Diameter/2 = 7 × 10⁻³ m

Finding the cross-sectional area:

Area = πr²

Area = (22 × 7 × 10⁻³ × 7 × 10⁻³)/7

Area = 154 × 10⁻⁶

∴ Cross-sectional area of wire = 154 × 10⁻⁶ m²

Finding the resistance of the wire:

We know that.

ρ = (A× R)/L

where,

ρ = Resistivity

R = Resistance = 44 × 10⁻⁸ Ω m

A = Cross-sectional = 154 × 10⁻⁶ m²

L = length = 15 × 10⁻² m

⟿ ρ = (154 × 10⁻⁶ × 44 × 10⁻⁸)/(15 × 10⁻²)

⟿ ρ = (154 × 10⁻⁶ × 44 × 10⁻⁸ × 10²)/15

⟿ ρ = ( 6776 × 10⁻¹²)/15

⟿ ρ = 451 × 10⁻¹² (approx.)

Answer 2

Explanation:

here data :- l = 150 m = 1.5m

diameter = 1mm = 1 × 10^-3m