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 Q.

Explanation:

Given that:

• A wire 150 cm long and diameter 14 mm is made of an alloy of resistivity 44 × 10-³0 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 x 10-¹ m

Length of wire = 15 × 10-¹ m

Finding the diameter of wire in metre:

• 1000 mm 1m

• 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 x 10-6

→ Cross-sectional area of wire = 154 x 10-6

.

Finding the resistance of the wire:

• We know that.

• R = (px L)/A

where,

• R = Resistance

• p = Resistivity = 44 x 10-8 m

• A = Cross-sectional = 154 × < 10-6 m²

• Llength = 15 × 10-¹ m

• R = (44 × 10-8 × 15 × 10-¹)/(154 × 10-9)
• R = (660 × 10-9)/(154 × 10-9)
• R = (4.3 × 10-9 × 10°)
• R = 43 x 10-4

→ Resistance of the wire 43 × 10-4 Q

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

$\sf\:Radius = Diameter/2$

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

$\sf \rho = RA/I$

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

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

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

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