Question

The electrical resistance of a wire varies directly as its length and inversely as the square of its diameter. a wire with a length of 200 inches and a diameter of one-quarter of an inch has a resistance of 20 ohms. find the electrical resistance in a 500 inch wire with the same diameter.

Answer 1

The electrical resistance of the wire is proportional to its length L and inversely proportional to the square of its diameter, $1/r^2$. 

The length of the wire in the problem is changed from 200 inches to 500 inches, so the new length is 2.5 times the initial length:
$\frac{L_1}{L_0}= \frac{500}{200}=2.5$
the diameter of the wire is not changed, so the new electrical resistance must be 2.5 times the original value:
$R_1 = 2.5 R_0 = 2.5 \cdot 20 \Omega =50 \Omega$