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:

$R=k\cdot\frac{L}{D^2}$

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:

$\begin{gathered} R=k\cdot\frac{L}{D^2} \\ k=\frac{R\cdot D^2}{L} \\ k=\frac{18737\cdot0.02^2}{4900} \\ k=\frac{18737\cdot0.0004}{4900} \\ k=\frac{7.4948}{4900} \end{gathered}$

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

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

Answer: the resistance is R = ohms.