Question

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. A wire with a length of 200 inches and a diameter of one-half of an inch has a resistance of 10 ohms. Find the electrical resistance in a 500 inch wire with the same diameter.

Group of answer choices

25 ohms

50 ohms

200 ohms

400 ohms

Answer 1

Data given:

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter.

A wire with a length of 200 inches and a diameter of one-half of an inch has a resistance of 10 ohms.

Electrical resistance in a 500 inch wire with the same diameter = ?

Let the length, diameter and the electrical resistance of the wire be represented by "l", "d" and "r" respectively.

Using the above information, we can find the equation that relates "l", "d" and "r" as -

1. The electrical resistance (r) of a wire varies directly as its length (l) and inversely as the square of its diameter (d).

   where k is the constant of proportionality.

2.  A wire with a length of 200 inches and a diameter of one-half of an inch has a resistance of 10 ohms.

  

On substituting these values in the equation obtained in part(1), we get -

Thus, the required expression is given by -

3. Now, we can compute the electrical resistance in a 500 inch wire with the same diameter (d = 0.5 inch) as -

  

  

  

Thus, the electrical resistance in a 500 inch wire with the diameter of one-half of an inch is 25 ohms.

Hence, the correct option is (A).