SOLUTION: 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 a

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 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 a      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 750403: 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.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+R+=+k%2AL%2A%28+1%2FD%29%5E2+
given:
+20+=+k%2A200%2A%281%2F.25%29%5E2+
+20+=+k%2A200%2A16+
+k+=+20%2F%28+200%2A16+%29+
+k+=+.00625+
-------------
+R+=+k%2A500%2A%28+1%2F.25%29%5E2+
+R+=+.00625%2A500%2A%28+1%2F.25%29%5E2+
+R+=+3.125%2A16+
+R+=+50+
The resistance is 50 ohms

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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.
:
let r = the resistance of a 500" wire
Since resistance varies directly with length and the diameter is the same we can:
r%2F20 = 500%2F200
Cross multiply
200r = 20*500
Divide thru by 20
10r = 500
r = 500/10
r = 50 ohms