rvc
  • rvc
Circuit question Please help :)
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
rvc
  • rvc
|dw:1440434594670:dw|
rvc
  • rvc
@rishavraj @IrishBoy123 @mathmate @Michele_Laino @e.mccormick please help :)
rvc
  • rvc
|dw:1440434946834:dw|

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arindameducationusc
  • arindameducationusc
wow... nice one.. i just had my dinner... was about to sleep.. would you mind if I do tomorrow morning?
IrishBoy123
  • IrishBoy123
i can have a try later today
Michele_Laino
  • Michele_Laino
I think that we have to apply the second and first principle of Kirchhoff
rvc
  • rvc
yep
Michele_Laino
  • Michele_Laino
|dw:1440436198619:dw| we have to suppose the existence of those currents, I1,...,I6
rvc
  • rvc
okay
Michele_Laino
  • Michele_Laino
now, we have to write the first principle of Kirchhoff at each node
rvc
  • rvc
incoming ccurrents= outgoing currents
Michele_Laino
  • Michele_Laino
yes! or algebraic sum of currents=0
rvc
  • rvc
yep
Michele_Laino
  • Michele_Laino
I label each node as below: |dw:1440436439762:dw|
rvc
  • rvc
oh okay
Michele_Laino
  • Michele_Laino
for node A: \[\Large {I_2} + 20 - {I_3} = 0\]
Michele_Laino
  • Michele_Laino
for node B: \[\Large {I_3} - {I_4} - 120 = 0\]
Michele_Laino
  • Michele_Laino
for node C: \[\Large {I_4} + 110 - {I_5} = 0\]
Michele_Laino
  • Michele_Laino
for node D \[\Large {I_5} - {I_6} - 60 = 0\]
Michele_Laino
  • Michele_Laino
for node Y: \[\Large {I_6} + 80 - {I_1} = 0\]
rvc
  • rvc
can we asume current through ab as I1 and ax as 20-I1 ?
Michele_Laino
  • Michele_Laino
for node X: \[\Large {I_1} - {I_2} - 30 = 0\]
Michele_Laino
  • Michele_Laino
with those equations, we have expressed the conservation of electrical charge
Michele_Laino
  • Michele_Laino
now, we have to happly the second principle of Kirchhoff, namely the subsequent equation for electrostatic field E: \[\Large \nabla \times {\mathbf{E}} = 0\] in order to do that we have to establish a positive sense into our circuit, like this: |dw:1440436999284:dw|
Michele_Laino
  • Michele_Laino
here is the missing equation: \[\large {V_{XY}} + 0.01{I_2} + 0.01{I_3} + 0.03{I_4} + 0.01{I_5} + 0.02{I_6} = 0\]
Michele_Laino
  • Michele_Laino
so, you have to determine all currents, I1,...,I6, then substituting into last equation, you will get the requested voltage drop Vxy
Michele_Laino
  • Michele_Laino
@rvc
mathmate
  • mathmate
Hmm, There are 6 equations for 7 unknowns! @Michele_Laino I put 5 equations for the joints (the sixth is redundant) and the Kirchhoff's second law as 0.02*I1+0.01*I2+0.01*I3+0.03*I4+0.01*I5+0.02*I6=0 instead of using Vxy, and I seem to get satisfactory results, with I4 and I6 negative. Do you get the similar results? @rvc
Michele_Laino
  • Michele_Laino
if we collect all those equations above, we get the complete system as below: \[\Large \left\{ \begin{gathered} {I_2} + 20 - {I_3} = 0 \hfill \\ \hfill \\ {I_3} - {I_4} - 120 = 0 \hfill \\ \hfill \\ {I_4} + 110 - {I_5} = 0 \hfill \\ \hfill \\ {I_5} - {I_6} - 60 = 0 \hfill \\ \hfill \\ {I_6} + 80 - {I_1} = 0 \hfill \\ \hfill \\ {I_1} - {I_2} - 30 = 0 \hfill \\ \hfill \\ {V_{XY}}{\text{ }} + {\text{ }}0.01{I_2}{\text{ }} + {\text{ }}0.01{I_3}{\text{ }} + {\text{ }} \hfill \\ {\text{ + }}0.03{I_4}{\text{ }} + {\text{ }}0.01{I_5}{\text{ }} + {\text{ }}0.02{I_6}{\text{ }} = {\text{ }}0 \hfill \\ \end{gathered} \right.\]
mathmate
  • mathmate
What I was saying is that there are 5 independent equations out of the first 6, so the last one will fill the void by expression Vxy as 0.02*I1. Then we get to have 6 equations, and 6 unknowns (I1 to I6).
IrishBoy123
  • IrishBoy123
yes, first 5 plus 0.02*I1+0.01*I2+0.01*I3+0.03*I4+0.01*I5+0.02*I6=0 gets there! [ 61. 31. 51. -69. 41. -19.]
mathmate
  • mathmate
Yep, I got the same answers.
mathmate
  • mathmate
Don't forget to find Vxy=61*0.02=1.22 V... etc.

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