The resistance of a wire varies directly with its length and inversely with the square of its diameter

Question

The resistance of a wire varies directly with its length and inversely with the square of its diameter. If 100 ft. Of wire with diameter of 0.01 in has a resistance of 10 OHMS, what is the resistance of 150 ft of the same type of wire if it's diameter is 0.02. Round to the nearest hundredth?

Answer 1

First let's set up an equation with some k constant. Since resistance is the main variable, we'll put that on the left side.

R = k•L/D²

Now let's plug in the first set of values: R=10, L=100, D=.01

10 = k•100/0.01² (Now we solve for k)

k=0.00001

Now plug in k, L, and D for the second set of values.

R = 0.00001•150/0.02²

R = 15/4 = 3.75 OHMS

Thus, the resistance of this new wire is 3.75 OHMS.