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

Question

resistance of 10 ohms, what is the resistance of 100 feet of the same type of wire if its diameter is 0.02 inch? Round to the nearest hundredth.

the resistance is ___ohms.

Answer 1

combined variation tells us:

 

Resistance = k(length) / diameter²

 

where 'k' is the constant of variation

 

we use the info for the first scenario to find 'k', then plug it in to solve for the second scenario.

 

10 ohms = k (100) / .01²

 

10 = (k)(10⁶)

 

k = 10^-5

 

knowing this, we can now plug into the same formula, with our newly found 'k' and the new data:

 

resistance = (10^-5)(100) / (.02²)

 

can you solve that?