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Electric circuits ?

Any help with this circuit? 

I want to prove that the total power dissipated equals the total power developed.

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2 Answers

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  • 1 month ago

    Notice that Vo = 3io*80 = 240io. 4Vo = 960io

    Let the current leaving the 100V source = i. KVL cw around the left loop 100-10i-20(i-io)-960io = 0

    -940io = 30i - 100

    io = (-3i +10)/94

    KVL around center loop:

    +960io+20i-20io-40io+120-240io = 0

    660io = -20i -120

    io = -(i+6)/33

    Solve for i by equating  (-3i +10)/94 = -(i+6)/33

    i(-3/94+1/33) = -10/94-6/33

    i = (-10/94-6/33)/(-3/94+1/33) = 178.8A out of 100V source

    io = (-3*178.8+10)/94 = -5.6A or +5.6A into 120V source

    Power delivered by sources:

    100*178.8+184.4*5376-120*5.6 - 2*5.6* (-1344) = 102.4MW

    Power consumed by resistance

    178.8²*10+184.4²*20+5.6²*40+16.8²*80 = 102.4MW checks.

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  • Roger
    Lv 7
    1 month ago

    The current through the 80 ohm resistor is 3(Io)

    Vo = 80(3Io) =(240)Io

     

    Let I1 be the current through the 100 volt source and let it flow upwards

    and I2 be the current in the dependent 4Vo source also flowing upward

     

    Io = I1 + I2  therefore I1 = Io - I2

    100 volts - 10I1 = 4Vo - 20I2

    100 volts = 4Vo +10I1 - 20I2

    100 volts = 4 Vo +10(Io -I2) - 20I2

    100 volts = 4(240Io) + 10Io - 30I2

    100 volts = 970Io - 30I2

    10 volts = 97Io -3I2     call this equation 1

    100 volts -10I1 -40Io +120 volts = Vo = 240(io)

    220 volts = 280(Io) +10(Io -I2)

    220 volts = 290(Io) - 10I2

    22 volts = 29Io - I2  call this equation 2

    Using both equations 1 and 2 solve for Io and I2

    Io = -5.6 amps

    I2 = -184.4 amps

    I1 = -5.6 -(-184.4) = 178.8 amps

    Vo = 3(Io)80= 240(-5.6)= -1,344 volts

    The 80 ohm resistor dissipates 22,579.2 watts  (= 3(-5.6)( -1,344))

    The 40 ohm resistor dissipates 1,254.4 watts  ( =( Io^2)(40))

    The 10 ohm resistor dissipates 319,694 watts   (= (I1^2)(10))

    And the 20 ohm resistor dissipates 680,067 watts  ( =(I2^2)(20))

    The 100 volt source  provides  17,880 watts  ( = 100 volts x 178.8 amps)

    The 120 volt source dissipates 672 watts since the current Io is flowing into the source. (-5.6 x 120)

    The 2 Io dependent current source  provides 15,053 watts  (= 2(-5.6 amps) x - 1,344 volts

    The 4 Vo dependent source provides 991.334 watts

    ( = 4Vo x I2) which is  4(-1,344 volts)(-184.4 amps)

    double check the math

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