Answer to Question #242880 in Electric Circuits for Neilmar

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

Explanations & Calculations

• Equivalent resistance in the first case is $\small R_e = R_a+R_b+R_c.$
• From the power of the circuit

$\qquad\qquad \begin{aligned} \small 200W&=\small \frac{V^2 }{R_e}=\frac{V^2}{R_a+R_b+R_c}\\ \small R_a+R_b+R_c&=\small \frac{120^2}{200}\\ &=\small 72\Omega\cdots(1) \end{aligned}$

• When they are connected in parallel the equivalent will be

$\qquad\qquad \begin{aligned} \small \frac{1}{R_{e1}}&=\small \frac{1}{R_a}+\frac{1}{R_b}+\frac{1}{R_c}\\ &=\small \frac{1}{R_a}+\frac{1}{2R_a}+\frac{1}{3R_a}\\ \small R_{e1}&=\small \frac{6R_a}{11} \cdots\cdots(2) \end{aligned}$

• Now, it is about calculating $\small R_a$, which can be done with the help of the equation (1).
• Give it a try & once you have the value, you can substitute it in equation (2) & get the required answer.