Use source transformation theory to Find?

Question

Vo and the power

developed by the 300V source, the power developed by the 10A current source and verify that the

total power developed equals the total power dissipated.

Answer 1

Circuit Simulator Applet

sources    E (v)    I(A)    P (W)

V            300    34.123    10237

I          125.118    10          1251

tot                                    11488

res            

4       136.493    34.123    4658.

6       163.507    27.251    4456.

40    -125.118      3.128      391.366

10       68.            6.872      472.249

24     164.929      6.872     1133.

8         54.976      6.872       377.799

tot                                        488.414

Answer 2

first let me correct the drawing to what I think is your intention, by adding a connection dot.

Then transform the current source and 40Ω resistor to a voltage source as shown.

combine the 4 resistors on the right to 82Ω

then use superposition to get voltage across the 6Ω, call it V1

V1 due to left source:

6 parallel to 82 = 6•82/88 = 5.591 Ω

V1 = 300(5.591/(5.591+4)) = 174.9 V

V1 due to right source:

6 parallel to 4 = 6•4/10 = 2.4 Ω

V1 = 400(2.4/(82+2.4)) = 11.3 V

total is sum, 186.2 V

current thru 6Ω = 186.2/6 = 31.0 amps

current in right loop (CW) is (400–186.2)/82 = 2.61 amps

current in left loop (CW) is (300–186.2)/4 = 28.45 amps

and the two add up to 31 amps

Vo = 2.61•24 = 62.6 volts

power from 300 v source = 300•28.45 = 8535 watts

power from 400 v source: = 400•2.61 = 1044 watts

  which is equal to power from 10 A source

you have all the currents, you can use I²R to get the power in each R and add them up.