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Superpostioning of an inpendent voltage and current source with depend

  • Thread starter cybhunter
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  • #1
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Homework Statement



3 branches, Indpendents are a 15 Volt source (left most branch) in series with a 2 ohm resistor (current that flows from left to right though this resistor is 'i delta'), Middle branch contains a 5 ohm resistor in series with a current controlled voltage source (3 ohms * i delta). The Right most branch has a 4 ohm resistor in series with a parallel configurtion of an 8 ampere source and a 8 ohm resistor (voltage across denoted as 'V0').

Find Vo, Find i delta


Homework Equations



using a superpostioning and source transformation properties I've been able to reconfigure the rightmost branch to a voltage source of 64 volts in series with a 12 ohm resistor



The Attempt at a Solution



Turning off the 64 volt source and leaving the 15 volt source on:

-15 volts+ 2ohms*(i delta) +5ohms* (i1-i2) +3ohm*(i delta)= 0 Volts (i1 and i2 are unknown currents the center branch, with the 3 ohm being the current controlled voltage source)

-3ohm*(i delta) -5ohms( i2-i1) -12ohms*(i2)=0 Volts



Turning off the 15 volt source and leaving the 64 volt source on:
-3ohm*(i delta) -5ohms(i2' -i1') -12 ohms*(i2')=0 Volts

-15 Volts +2ohms*(i delta)+ 5ohms(i1' -i2')+ 3ohm*(i delta)=0 Volts

I end up stuck at this point
 

Answers and Replies

  • #2
gneill
Mentor
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2,759


Homework Statement



3 branches, Indpendents are a 15 Volt source (left most branch) in series with a 2 ohm resistor (current that flows from left to right though this resistor is 'i delta'), Middle branch contains a 5 ohm resistor in series with a current controlled voltage source (3 ohms * i delta). The Right most branch has a 4 ohm resistor in series with a parallel configurtion of an 8 ampere source and a 8 ohm resistor (voltage across denoted as 'V0').

Find Vo, Find i delta


Homework Equations



using a superpostioning and source transformation properties I've been able to reconfigure the rightmost branch to a voltage source of 64 volts in series with a 12 ohm resistor



The Attempt at a Solution



Turning off the 64 volt source and leaving the 15 volt source on:

-15 volts+ 2ohms*(i delta) +5ohms* (i1-i2) +3ohm*(i delta)= 0 Volts (i1 and i2 are unknown currents the center branch, with the 3 ohm being the current controlled voltage source)

-3ohm*(i delta) -5ohms( i2-i1) -12ohms*(i2)=0 Volts



Turning off the 15 volt source and leaving the 64 volt source on:
-3ohm*(i delta) -5ohms(i2' -i1') -12 ohms*(i2')=0 Volts

-15 Volts +2ohms*(i delta)+ 5ohms(i1' -i2')+ 3ohm*(i delta)=0 Volts

I end up stuck at this point
It looks like you're doing mesh analysis with one source active at a time. That's fine.

Note that iΔ flowing through the 2Ω resistor is identical to the mesh current i1. So you can make that substitution for iΔ. You should be able to determine numerical values for the mesh currents (and thus determine iΔ and Vo) for either source being active.
 
  • #3
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If there was a thanks button, I just clicked it for you. Thanks for noting the correlation between the i delta and i1 currents
 
  • #4
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As a followup, I decided to upload the problem with my explanation to the problem. Hope it provides help to anybody needing some guidance (and thanks again gneill)
 

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