:Calculating $k$ to Find Wire Length

[karush]

$\tiny{2.5.1}$
Electrical Resistance of a Wire
The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire.
If a wire 432 feet long and 4 mm in diameter has a resistance of 1.24 $\Omega$
find the length of a wire of the same material whose resistance is 1.44 $\Omega$ and whose diameter is 3 mm

y varies inversely with x $\quad y=\dfrac{k}{x}$
y varies directly with x $\quad y=kx$

OK not real sure how to set this up think we need to get the value of $k$ first

 

[topsquark]

Well, by the problem statement \(\displaystyle R \propto L\) and \(\displaystyle R \propto \dfrac{1}{d^2}\). Thus
\(\displaystyle R = k \dfrac{L}{d^2}\)

Is this what you were asking about?

-Dan

 

[karush]

yes,

 

[karush]

$1.24 = k \dfrac{L}{d^2}=k \dfrac{432}{(4)^2}$

$k=0.04592$

so far hopefully

added to Google calendar

 

[topsquark]

$1.24 = k \dfrac{L}{d^2}=k \dfrac{432}{(4)^2}$

$k=0.04592$

so far hopefully

added to Google calendar

Units! (They are really weird units.) This is a Physics problem. All quantities with units must be stated with what they are.

So far so good. So use \(\displaystyle R = k \dfrac{L}{d^2}\) again to find R.

-Dan

 

[HOI]

$\tiny{2.5.1}$
Electrical Resistance of a Wire
The electrical resistance of a wire varies directly with the length of the wire and inversely with the square of the diameter of the wire.
If a wire 432 feet long and 4 mm in diameter has a resistance of 1.24 $\Omega$
find the length of a wire of the same material whose resistance is 1.44 $\Omega$ and whose diameter is 3 mm

y varies inversely with x $\quad y=\dfrac{k}{x}$
y varies directly with x $\quad y=kx$

OK not real sure how to set this up think we need to get the value of $k$ first

Do you understand that you need ONE equation, not two? And of course you don't want to use "x" for both length and diameter.

Letting "R" be electrical resistance", L be the length, and D the diameter of the wire, since R varie directly with L and inversely with the square D,
$R= k\frac{L}{D^2}$.

Now, yes, you need to find k. For that you need to know every thing except k.
You are told "a wire 432 feet long and 4 mm in diameter has a resistance of 1.24 Ω".
So $1.24= k\frac{432}{4^2}$. Solve that for k.