Ohms

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iragarcia24

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A wire has resistance of 5 ohms. What will be the resistance of another wire the same material three times as long and HALF the cross sectional area?

Answer is 30 Ohms. Can someone explain this to me?


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Length of a conductor and cross section are proportional.

If the wire with 5 ohms resistance is 1' long than a 3' piece will be 3 times more resistive. 3 x 5 = 15.

If the cross section of the conductor is halved the resistance is doubled, and vice versa.

So now you have 15 ohms x 2 = 30 ohms.
 
jumper said:
Length of a conductor and cross section are proportional.

If the wire with 5 ohms resistance is 1' long than a 3' piece will be 3 times more resistive. 3 x 5 = 15.

If the cross section of the conductor is halved the resistance is doubled, and vice versa.

So now you have 15 ohms x 2 = 30 ohms.
Click to expand...

So in theory if the sizes of the conductor went up by half I would multiply by .5 instead of 2?


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iragarcia24 said:
So in theory if the sizes of the conductor went up by half I would multiply by .5 instead of 2?
Click to expand...
No. If the conductor cross sectional area increases by 50% the resistance goes down by 33%, or to to 67% of the original. Look at Table 8 and compare the resistance of 600kcmil copper to 400kcmil copper. Resistance is inversely proportional to cross sectional area; the area ratio is 3/2 and the reciprocal is 2/3, or .67.
 
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iragarcia24 said:
So in theory if the sizes of the conductor went up by half I would multiply by .5 instead of 2?


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Click to expand...


An increase of 50%, on an increase by half, really means you multiply the original value by 150% (or 1.5). It is a deceptive way we speak about the change in a value.

A better way to say it, is "the value increased by a factor of 2", which means you multiply the original value by 2. Indeed if you increase cross sectional area by a factor of 2, then you half the resistance.
 
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