Chapter 1, Problem 1P

To determine

Find the number of kilograms of conductors in the line.

Answer to Problem 1P

The number of kilograms of conductors in the line is $20.5\times {10}^6\text{kg}$.

Explanation of Solution

Given data:

The number of conductors in line is four.

The weight of each conductor $\left(w\right)$ is $\frac{\text{2526}\text{lb}}{\text{1000}\text{ft}}$.

The length of line $\left(l\right)$ is $845\text{miles}$.

Formula used:

Write a general expression that shows the relation between ‘mile and ft’, and ‘kg and lb’.

$1\text{mile}=5280\text{ft}$

$1\text{kg}=2.2\text{lb}$

Calculation:

The weight of conductor is calculated as follows,

$\text{ Weight of conductor}\left(W\right)=wl$ (1)

Substitute $\frac{\text{2526}\text{lb}}{\text{1000}\text{ft}}$ for $w$, and $845\text{miles}$ for $l$ in equation (1) to find $W$.

$\text{ Weight of conductor}\left(W\right)=\left(\frac{\text{2526}\text{lb}}{\text{1000}\text{ft}}\right)\left(845\text{miles}\right)$ (2)

Using product of ratios, convert the unit of equation (2) from $\frac{\text{lb}}{\text{ft}}\cdot \text{miles}$ to $\text{kg}$ to find $W$.

$\begin{array}{c}W=\left(845\text{miles}\right)\left(\frac{\text{2526}\text{lb}}{\text{1000}\text{ft}}\right)\cdot \left(\frac{5280\text{ft}}{1\text{mile}}\right)\cdot \left(\frac{1\text{kg}}{2.2\text{lb}}\right)\\ =5122728\text{kg}\end{array}$

The total weight of four conductors can be calculated as follows,

$W_T=4W$ (3)

Substitute $5122728\text{kg}$ for $W$ in equation (3) to find $W_T$.

$\begin{array}{c}{W}_T=4\left(5122728\text{kg}\right)\\ =20.5\times {10}^6\text{kg}\end{array}$

Conclusion:

Thus, the number of kilograms of conductors in the line is $20.5\times {10}^6\text{kg}$.