Question

A wire 150 cm long and diameter 1 mm is made of an alloy of resistivity 44 into 10 to the power minus 8 ohm metre what is the resistance of the wire?

Ps: how to convert 1mm to m

Answer 1

Resistance = rho(resistivity) x length / area of the cross section

Resistance = 44 x 10(-8) x 150 / 0.001

Resistance = 600 x 10(-8) / 0.001

Resistance = 6 x 10(-6) /0.001

Resistance = 6 x 10(-6) x 1000 / 0.001

Resistance = 6 x 10 (-3) /1

Resistance =6 x 10 power minus 3 ohm

Answer 2

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 metre:

100 cm = 1 m

150 cm = 150/100 = 15 × 10⁻² m

∴ Length of wire = 15 × 10⁻² m

Finding the diameter of wire in metre:

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.)

∴ Resistance of the wire = 451 × 10⁻¹² Ω