Question

The resistance, R, of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a wire 4900ft long with a diameter of 0.02 inches is 18737 ohms, what is the resistance of 3900ft of the same type of wire with a diameter of 0.06 inches? (Leave k in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredth.)

Answer 1

We know that the resistance R varies proportionally to the wire's length L and inveresly to the square of its diameter D.

We can express this as:

`R=k\cdot(L)/(D^2)`

where k is a constant.

We can calculate the value of k using the expression above and knowing that R = 18,737 ohms when L = 4,900 ft and D = 0.02 in.

We replace with the values and calculate k as:

`\begin{gathered} R=k\cdot(L)/(D^2) \\ k=(R\cdot D^2)/(L) \\ k=(18737\cdot0.02^2)/(4900) \\ k=(18737\cdot0.0004)/(4900) \\ k=(7.4948)/(4900) \end{gathered}`

We then can calculate the resistance for a wire with length L = 3900 ft and diameter D = 0.06 as:

`\begin{gathered} R=0.00153\cdot(L)/(D^2) \\ R=0.00153\cdot(3900)/((0.06)^2) \\ R=0.00153\cdot(3900)/(0.0036) \\ R=1657.5 \end{gathered}`

Answer: the resistance is R = ohms.