Chapter 2, Problem 26P

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

$R_2=\frac{R_b{R}_c}{R_a+R_b+R_c}$ (2.69)

(a) Suppose $R_2=12$. $R_a=R$, $R_b=3R$, and $R_c=100+R$, all measured in ohms. Substitute these values into equation (2.70) to obtain the following quadratic equation for R. $R^2+40R-1200=0$

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