Question

A wire 150 cm long and diameter 14 mm is made of an alloy of resistivity 44x10 -8Ohm m.What is the resistance of the wire ?​

Answer 1

Answer:

• Resistance of the wire is 43 × 10⁻⁴ 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 × 10⁻¹ m

∴ Length of wire = 15 × 10⁻¹ 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.

• R = (ρ × L)/A

where,

• R = Resistance
• ρ = Resistivity = 44 × 10⁻⁸ Ω m
• A = Cross-sectional = 154 × 10⁻⁶ m²
• L = length = 15 × 10⁻¹ m

⟿ R = (44 × 10⁻⁸ × 15 × 10⁻¹)/(154 × 10⁻⁶)

⟿ R = (660 × 10⁻⁹)/(154 × 10⁻⁶)

⟿ R = (4.3 × 10⁻⁹ × 10⁶)

⟿ R = 43 × 10⁻⁴

∴ Resistance of the wire = 43 × 10⁻⁴ Ω

Answer 2

Given :-

A  wire 150 cm long and diameter 14 mm is made of an alloy of resistivity  44x10  -8Ohm m.

To Find :-

Resistance

Solution :-

At first

Wire in meter = 1.5 m = 15 × 10⁻²

Now

For diameter =  14 × 10⁻³ m

Radius = Diameter/2

Radius = 14 × 10⁻³/2

Radius = 7 × 10⁻³

$\sf Area = \pi r^2$

$\sf Area = \dfrac{22}{7} \times{ 7 \times 10^{-3}}^2$

$\sf Area = \dfrac{22}{7}\times 7\times10^{-3}\times 7 \times10^{-3}$

$\sf Area = 22 \times 10^{-3}\times7\times10^{-3}$

$\sf Area = 154\times 10^{-6}$

According to the question

$\sf \rho = RA/I$

$\sf \rho = \dfrac{154 \times 10^{-6} \times 44 \times 10^{-8}}{15 \times 10^{-2}}$

$\sf \rho = \dfrac{6776\times 10^{-14}}{15 \times 10^{-2}}$

$\sf \rho = \dfrac{6776 \times 10^{-12} \times 10^{2}}{15}$

$\sf \rho = 451 \times 10^{-12}$