Chapter A.5, Problem 44AYU

To determine

To find: Express $R$ as a rational expression.

Answer to Problem 44AYU

$\frac{20}{11}$

Explanation of Solution

Given:

The formula,

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$

$R_1=5$

$R_2=4$

$R_3=10$

Calculation:

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}=\frac{R_2.R_3+R_1.R_3+R_1.R_2}{R_1.R_2{R}_3}$

$R=\frac{R_1.R_2{R}_3}{ R_2.R_3+R_1.R_3+R_1.R_2}=\frac{\left(5\right).\left(4\right).\left(10\right)}{4.10+5.10+5.4}=\frac{20}{ 11}$