Question

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 433 feet long and 4 millimeters in diameter has a resistance of 1 .24 ohms, find the length of a wire whose resistance is 1.49 ohms and whose diameter is 5 millimeters.

Answer 1

Given:

The length of the wire is,

`l=433\text{ feet}`

The diameter of the wire is,

`d=4\text{ mm}`

The resistance of the wire is,

`R=1.24\text{ ohms}`

To find:

The length of the wire whose resistance is,

`R^(\prime)=1.49\text{ ohms}`

diameter is,

`d^(\prime)=5\text{ mm}`

Step-by-step explanation:

The resistance of a conductor is,

`R\propto(l)/(d^2)`

We can write,

`\begin{gathered} (R)/(R^(\prime))=(l)/(l^(\prime))*(d^(\prime2))/(d^2) \\ (1.24)/(1.49)=(433)/(l^(\prime))*(5^2)/(4^2) \\ l^(\prime)=433*(25)/(16)*(1.49)/(1.24) \end{gathered}`

The length is,

`l^(\prime)=813\text{ feet}`

Hence, the required length is 813 feet.