Question

A copper wire has diameter 0.5 mm and resistivity of (1.6*10)-8ohm find length

Answer 1

Correct Question :-

✓✓ A copper wire has a diameter of 0.5 mm and resistivity of 1.6 × 10^-8 Ω m. What will be the length of this wire to make it's resistance 10 Ω ?

Given:-

• Diameter = 0.5 mm
• Radius = d/2
• Radius = 0.5/2 mm = 0.25 mm

This radius of 0.25 mm will be equal to 0.25/1000 m or 0.25 × 10^-3 m.

To Find :-

• The length of this wire to make it's resistance 10 Ω = ?

Solution:-

☞ At first we will now find out the area of cross section of the copper wire by using this value of the radius. so,

Area of cross section of wire = πr²

$\bf\:=\dfrac{22}{7}\times\:(0.25\times\:{10}^{-3})^2$

$\bf\:=0.1964\times\:{10}^{-6}\:{m}^{2}$

Now,

• Resistivity (ρ) $\bf\:=1.6\times\:{10}^{-8}\:ohm\:m$

• Resistance (R) = 10Ω

• Length = ?

Now, putting this values in the formula:-

ρ$\bf\:=\dfrac{R\times\:A}{L}$

we get,$\bf\:1.6\times\:{10}^{-8}=\dfrac{10\times\:0.1964\times\:{10}^{-6}}{L}$

$\bf\implies\:L=\dfrac{10\times\:0.1964\times\:{10}^{-6}}{1.6\times\:{10}^{-8}}$

$\bf\implies\:L=\dfrac{1964}{16}$

$\bf\implies\:L=122.7\:m$

Thus, the length of copper wire required to make 10Ω resistance will be 122.7m