Answer:
0.1213 ohms
Step-by-step explanation:
If a quantity, A, varies inversely as the square of another quantity, B, we can write the proportionality equation as:
[tex]A=\frac{k}{B^2}[/tex]
In our problem, we have,
Resistance varies inversely as the square of Diameter
Let resistance be r and diameter be d, so we can write:
[tex]r=\frac{k}{d^2}[/tex]
Where
k is the proportionality constant to be found
Now, it is given that
r = 0.447
d = 0.01
We substitute and find k:
[tex]r=\frac{k}{d^2}\\0.447=\frac{k}{0.01^2}\\0.447=\frac{k}{0.0001}\\k=0.0001*0.447\\k=0.0000447[/tex]
Again, we need to solve for r, given k = 0.0000447 and now d = 0.0192. Thus, we have:
[tex]r=\frac{k}{d^2}\\r=\frac{0.0000447}{0.0192^2}\\r=0.1213[/tex]
The resistance is 0.1213 ohms
