Question

Three resistors Ra,Rb,& Rc are connected in series to a 120volt source, and the total power taken by the
circuit is 200 watts. Rb = 2Ra, Rc =3Ra. If Ra,Ra,& Rc are connected in parallel, the equivalent resistance
will be?

Answer 1

The power disipated in circuit

$$P_1=\frac{V^2}{R_{\rm net 1}}=\frac{V^2}{R_{a}+R_b+R_c}=\frac{V^2}{6R_{a}}$$

Hence

$$R_a=\frac{V^2}{6P_1}=\frac{120^2}{6*200}=12\:\Omega$$

The equivalent resictance for the parallel circuit

$$R=\frac{1}{\frac{1}{R_a}+\frac{1}{R_b}+\frac{1}{R_c}}$$

$$R=\frac{1}{\frac{1}{12}+\frac{1}{2*12}+\frac{1}{3*12}}=6.5\:\Omega$$