Chapter 2, Problem 24P

When converting resistances connected in a ∆ formation to a Y formation as shown in Fig. P2.24, the resistance R ₂ is obtained as

$R_1=\frac{R_b{R}_c}{R_a+R_b+R_c}$ (2.68)

(a) Suppose $R_1=100$, $R_a=R_b=R$, and $R_c=100+R$, all measured in ohms. Substitute these values into equation (2.70) to obtain the following quadratic equation for R. $R^2-300R-10,000=0$

(b) Solve the quadratic equation for R by the methods of completing the square and the quadratic formula.