Given the circuit shown in the attachment find: values and power dissipated.
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I call 200 V V in my work to follow, 40 ohms is R1 , 300 ohms is Ra, and 75 ohms is Rb. ia + ib goes through V and R1. ia goes through Ra and ib goes through Rb. Vo is an unknown potential and ia and ib are unknown currents.
I know charge and currents are conserved.
Potential is conserved/
The power delivered by the potential elements is lost in the resistors of this circuit as the current moves through them.
So I have some circuit equations 1) V-(ia + ib)R1 -iaRa = 0
2) V-(ia + ib)R1 = Vo
3) V(ia + ib) + Voib = P P is the power
4) (ia + ib)^2 R1 + ia^2Ra + ib^2Rb = P
and then I worried as I see a quadratic that I am going to have to solve in ia or ib and I spent about two hours wrestling with this to find that the quadratic collapses as the constant term goes to zero ...
This solution is provided in 797 words. It uses circuit equations to solve for all of the problems.