Question

In the electric currect​ flow, it is found that the resistance​ (measured in the units called​ ohms) offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. If a wire 0.01 in. in diameter has a resistance of 0.447 ​ohms, what is the resistance of a wire of the same length and material with diameter 0.0192 in. to the nearest​ ten-thousandth?

Answer 1

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:

$A=\frac{k}{B^2}$

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:

$r=\frac{k}{d^2}$

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:

$r=\frac{k}{d^2}\\0.447=\frac{k}{0.01^2}\\0.447=\frac{k}{0.0001}\\k=0.0001*0.447\\k=0.0000447$

Again, we need to solve for r, given k = 0.0000447 and now d = 0.0192. Thus, we have:

$r=\frac{k}{d^2}\\r=\frac{0.0000447}{0.0192^2}\\r=0.1213$

The resistance is 0.1213 ohms