Use source transformation theory to Find?

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.

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2 Answers

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  • 2 months ago

    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

  • 2 months ago

    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.

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