Question 72966: the resistance of an electric wire is directly proportional to the length of the wire and inversely proportional to the square of the diameter. Write a formula expressing this property using R for resistance, L for length, and D for diameter.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's write the equation first and then we'll discuss it.
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The equation is:
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where R, L, and D are as defined in your problem and k is something we'll call a constant
of proportionality.
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The first thing to notice is that L is in the numerator of the fraction. As a result, when
L gets bigger then R will also get bigger. This is called "directly proportional."
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Then you need to notice that D is in the denominator. (As a matter-of-fact D squared is
in the denominator.) As a result, when D gets bigger, R will get smaller. This is called
inversely proportional.
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You can sort of get the idea by saying that if the diameter were 1, then the resistance
would be k*L. But if the diameter were 100, then the resistance would be k*L divided by
100. So the resistance would be considerably smaller.
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k is just something that is thrown in to make the equation balance. It accommodates such
things as the type of wire (for example, steel wire or copper wire). It also takes into account
the units of measurement. For example the length may be in meters, or yards, or feet,
and the wire size may be millimeters, inches, mils, or specific wire gauges. These could
all change on you and the basic equation would stay the same, but the value of k would change.
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Hope this helps you to understand the problem a little better.
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