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 80 ohms, wha

Question 209297: 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 80 ohms, what is the resistance of 90 feet of the same type of wire if its diameter is 0.04 inch?
HELP!!! I dont know what to do!
Found 3 solutions by stanbon, RAY100, Earlsdon:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
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 80 ohms, what is the resistance of 90 feet of the same type of wire if its diameter is 0.04 inch?
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r = k*L/D^2
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Find "k":
80 = k*100/0.01^2
80 = k*100/0.0001
80 = k/1,000,000
k = 80,000,000
-------------------------
Now you know the equation is
r = (80,000,000)L/D^2
---
what is the resistance of 90 feet of the same type of wire if its diameter is 0.04 inch?
r = (80,000,000)90/(0.04)^2
r = 4.5x10^12 ohms
========================
Cheers,
Stan H.
Answer by RAY100(1637)   (Show Source): You can put this solution on YOUR website!
From statements about direct and indirect variation,,,
.
R=k (L/d^2),,,where,,R= resistance(ohms),,,L=Length(ft),,,d=diameter(in)
.
and k is a constant of variation.
.
.
From example given,,,R=k (100/.01^2) =80,,,or k=.00008
.
Question is,,,R = k (90/.04^2)= .00008 (90/.04^2) = 4.5 ohms
.

Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
First, write the equation of variation for the resistance, R:
where L = length of the wire, d = the diameter of the wire, and k = the constant of variation.
Now substitute the given values of L (100 ft.), R (80 ohms) and d (0.01 inch) in order to find the value of k.

Now you can solve on the problem given:
Substitute: k = 0.00008, L = 90, and d = 0.04

ohms.
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