resistance calc.

[Chad304]

ran into a calculation question on resistance. Question is as follows. A conductor of 117 feet in length and 980 sq. mils csa has a resistance of 1 ohm. What is the resistance of 1987 feet of wire of 9862 sq mils of csa? assuming i was supposed to use the first part of the question to figure out what kind of conductor im dealing with. I used the formula R= pL/a. I plugged in 12.9 for copper wire, converted sq mils(980) into circular mils (1248) and came up with 1.2 ohms . I did the same with the 1987 feet of wire with 9862 sq mils and came up with 2 ohms. Am i correct? any help is appreciated

 

[Smart $]

ran into a calculation question on resistance. Question is as follows. A conductor of 117 feet in length and 980 sq. mils csa has a resistance of 1 ohm. What is the resistance of 1987 feet of wire of 9862 sq mils of csa? assuming i was supposed to use the first part of the question to figure out what kind of conductor im dealing with. I used the formula R= pL/a. I plugged in 12.9 for copper wire, converted sq mils(980) into circular mils (1248) and came up with 1.2 ohms . I did the same with the 1987 feet of wire with 9862 sq mils and came up with 2 ohms. Am i correct? any help is appreciated

Why convert? (redundant)

You have two scenarios in the same units. While the standard units for the R=pl/A formula are different, you don't need to convert because you are using the same unit for both scenarios (i.e. the ratios will be the same no matter what unit is used). With two scenarios of the same conductor material, p, the electrical resistivity is identical. Transposing the formula back to its original form we have:

p=RA/l

And thus....

R₁A₁/l₁ = R₂A₂/l₂

 

[Julius Right]

First conductor resistance has to be 1.24 ohm at 20oC[68 oF]. At 12oC[53.6oF] it is 1.2 indeed.
The second has to be 2.09 ohm at 20oC[68 oF]and 2 at 12oC[53.6 oF].

 

[Smart $]

First conductor resistance has to be 1.24 ohm at 20oC[68 oF]. At 12oC[53.6oF] it is 1.2 indeed.
The second has to be 2.09 ohm at 20oC[68 oF]and 2 at 12oC[53.6 oF].

That may be what it calculates out to (I did not check the math), but you have to use what is given as a constant in the question... as a constant. The question gives 1 ohm for the first conductor as a constant. Furthermore, question does not state that temperature is a variable. One should assume variable conditions not stated are not variable, i.e. constant, as well.

 

[wwhitney]

ran into a calculation question on resistance. Question is as follows. A conductor of 117 feet in length and 980 sq. mils csa has a resistance of 1 ohm. What is the resistance of 1987 feet of wire of 9862 sq mils of csa?

Smart$ gave you the algebra but if you don't like algebra you can think of it this way:

We're given that the resistance of 117 feet of 980 sq mils conductor is 1 ohm.

Resistance is proportional to length, so the resistance of 1987 feet of 980 sq mils conductor is (1987/117) * 1 ohm = 17.0 ohms. (Check: the resistance went up as expected)

Resistance is is inversely proportional to area, so the resistance of 1987 feet of 9862 sq mils conductor is (980/9862) * 17.0 ohms = 1.69 ohms. (Check: the resistance went down as expected)

I broke it down into two steps, first changing the length, then changing the area. You could do it in the opposite order and get the same result, since multiplication is commutative.

Cheers, Wayne

 

[charlie b]

To the other algebra-related comments I will add that the question did not say the conductor was made of copper. So you should not be using the 12.9 number anyway.