Question #243401

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?

circuit is 200 watts. Rb = 2Ra, Rc =3Ra. If Ra,Ra,& Rc are connected in parallel, the equivalent resistance

will be?

Expert's answer

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\:\OmegaThe 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

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