Chapter 2, Problem 6P

In the purely resistive circuit shown in Fig. P2.6, the total resistance R of the circuit is given by

$R=R_1+\frac{R_1{R}_2}{R_1+R_2}$ (2.58)

If the total resistance of the circuit is $R=100\Omega$ and $R_2=2R_1+100\Omega$. find

$R_2$ and $R_1$ as follows:

(a) Substitute the values of R and $R_2$ into equation (2.58), and simplify the resulting expression to obtain a single quadrate equation for $R_1$. (b) Using the method of your choice, solve the quadratic equation for $R_1$ and compute the corresponding value of $R_2$.