Answer to Question #243401 in Electrical Engineering for Neilmar

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?
1
Expert's answer
2021-09-29T04:38:26-0400

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"


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