solve the problem

Question

the resisitance of a no.8 copper wire whose cross section is 8.37mm^2 is 2.06 ohms per kilometer.

a. what is the resistance in ohms per 1000 ft?
b. what is the cross section in square inches?

Answer 1

You know that the resistivity formula is

 

R = ρL / A

 

where:

R = resistance of the wire

ρ = resistivity of the wire

L = length of wire

A = cross-section area of wire

 

Given:

ρ = 2.06 Ω•km

A = 8.37 mm²

 

But you won't have to actually use the formula.  You just need to perform some conversions.

 

a)

 

Convert the given value resistivity to Ω•1000 ft

 

 

b)

 

Convert the given value of area to in².

 

 

Use the conversion factor

 

1 in = (1/12) ft = 2.54 cm

Answer 2

Hi Danish,

 

Most of the questions you are asking have to do with unit conversions.

 

1 km = 1000 m

1 m = 100 cm = 1000 mm

1 in = 2.54 cm

1 ft = 12 in

 

a. To answer this question, we need to convert kilometers to feet.

 

(2.06 Ohms / km) * (1 km / 1000 m) * (1 m / 100 cm) * (2.54 cm / 1 in) * (12 in / 1 ft)

 

≈ 6.28 * 10^(-1) Ohms / 1000ft

 

b. Now we need to convert the cross sectional area from mm^2 to in^2. To simplify the units squaring, I will square the fraction as seen below:

 

8.37 mm^2 * (0.1 cm / mm)^2 * (1 in / 2.54 cm)^2

 

≈ 1.30  * 10^(-2) in^2

 

Hope this helps!