Given that the resistance, R, of a wire is inversely proportional to the square of its diameter, d, we can express this relationship as:

R = k/(d^2)

where k is the constant of proportionality.

From the problem, we know that when the diameter of the wire is 1 mm, its resistance is 15 ohms. We can use this information to find the value of k:

15 = k/(1^2)
= k = 15

Now we know that k = 15, we can use this value to find the diameter of a wire whose resistance is 60 ohms:

60 = 15/(d^2)
= d^2 = 15/60
= d^2 = 0.25
= d = sqrt(0.25)
= d = 0.5 mm

So, the diameter of a wire whose resistance is 60 ohms is 0.5 mm.

Question

Given that the resistance, R, of a wire is inversely proportional to the square of its diameter, d, we can express this relationship as:

R = k/(d^2)

where k is the constant of proportionality.

From the problem, we know that when the diameter of the wire is 1 mm, its resistance is 15 ohms. We can use this information to find the value of k:

15 = k/(1^2)
=> k = 15

Now we know that k = 15, we can use this value to find the diameter of a wire whose resistance is 60 ohms:

60 = 15/(d^2)
=> d^2 = 15/60
=> d^2 = 0.25
=> d = sqrt(0.25)
=> d = 0.5 mm

So, the diameter of a wire whose resistance is 60 ohms is 0.5 mm.

Knowee AI · Accepted Answer