SOLUTION: At a fixed temperature, the resistance R of a wire varies directly as the length 1 and inversely as the square of its diameter d. If the resistance is 1.2 ohm when the diameter is

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Question 1083857: At a fixed temperature, the resistance R of a wire varies directly as the length 1 and inversely as the square of its diameter d. If the resistance is 1.2 ohm when the diameter is 1 mm and the length is 240 cm, what is the resistance when the diameter is 3 mm and the length is 610 cm?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the direct variation formula is y = k * x

the indirect variation formula is y = k / x

the combined direct and indirect variation formula is z = k * x / y

replace z with R and replace x with L and replace Y with D^2 and the formula becomes:


R = k * L / D^2

R is equal to 1.2 when L is 240 and d is 1.

formula becomes 1.2 = k * 240 / 1^2

solve for k to get k = 1.2 * 1^2 / 240 = 1.2 / 240 = .005

that's the value of k which is the constant of variation.

it remains the same regardless of the values of R or D or L.

when d = 3 and L = 610, and k = .005, the formula becomes R = .005 * 610 / 3^2.

this results in R = .3389 ohms.








Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

At a fixed temperature, the resistance R of a wire varies directly as the length 1 and inversely as the square of its diameter d. If the resistance is 1.2 ohm when the diameter is 1 mm and the length is 240 cm, what is the resistance when the diameter is 3 mm and the length is 610 cm?
With R being resistance, L being length, D being diameter, and k, the CONSTANT of PROPORTIONALITY, you need to use the formula: 

Before you do so though, you need to convert the units from cm to mm, or vice-versa.

After finding k, substitute the cm or mm values for diameter and length to find R, the resistance. 

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