Calculate the resistance of wire 10 m long that has a diameter of 2 mm and resistivity of 2.63 ï½˜ 10⁻² Î© m. Answer (83715.3  Ω)



Given:

Length of wire =  L = 10 m

Diameter of wire =  D = 2 mm = 2 ｘ 10⁻³ m

Radius of wire =  r = `\frac {D}{2}` = `\frac {2 ｘ 10⁻³ m} = 1 ï½˜ 10⁻³ m
Resistivity of the wire = የ = 2.63 ï½˜ 10⁻² Ωm

To Find:

Resistance of wire = R = ?

Solution:


The formula for finding the Resistance R according to the given data is 

R = የ  `\frac {L}{A}` ----------(1)

where cross sectional area = A = ã„« r² = (3.1416)( 1 ï½˜ 10⁻³ m)² = 3.1416 ｘ 10⁻⁶ m² 

Now putting values in equation (1)


R = 2.63 ï½˜ 10⁻² Ωm ｘ `\frac {10 m}{3.1416 ｘ 10⁻⁶ m² }`

R = 2.63 ï½˜ 10⁻² Ωm ｘ 3.183 ｘ 10⁶ m⁻¹

R = 8.37153 ｘ 10⁻²⁺⁶ Ω

R = 8.37153 ｘ 10⁴ Ω

or

R = 83715.3  Ω ------------Ans.



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