SOLUTION: 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 90 ohms, wha

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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 90 ohms, wha      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 588576: 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 90 ohms, what is the resistance of 68 feet of the same type of wire if its diameter is 0.02 inch?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let L equal the length of the wire and let D equal the diameter of the wire.
let R equal the resistance of the wire.
the formula would be:
R = k * L / D^2
you know that 100 fee of wire with a diameter of .01 inches has a resistance of 90 ohms.
you can use this fact to find k, since k is a constant and will not vary.
your equation of:
R = k * L / D^2 becomes:
90 = k * 100 / (.01)^2
if you multiply both sides of this equation by (.01)^2 / 100 then you get:
90 * (.01)^2 / 100 = k
solve for k to get:
k = .00009
your formula of:
R = k * L / D^2 becomes:
R = .00009 * L / D^2
test this formula out with your original measurements to get:
R = .00009 * 100 / (.01)^2 and you will get:
R = 90 ohms.
use this formula with your new measurements and you will get:
R = .00009 * 68 / (.02)^2 which becomes:
R = 15.3 ohms.