please help!

Question

I dont understand this problem?

The resistance of a wire varies directly with its length and inversely with the square of its diameter. If 100 feet of wire with diameter 0.01 inch has a resistance of 40 ohms, what is the resistance of 56 feet of the same type of wire if its diameter is 0.04 inch?

Answer 1

Let r = resistance

     L = length

     d = diameter

 

Then, r = kL/d², for some constant, k.

 

r = 40 when L = 100 and d = 0.01, so 40 = k(100)/(0.01)²

 

                                                       k = 0.00004

 

r = 0.00004L/d²

 

So, if L = 56 and d = 0.04, then r = 0.00004(56)/(0.04)²

 

                                               = 1.4 Ω