Physics Help Forum KCl and simultaneus equations
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 Jun 4th 2009, 04:40 PM #1 Junior Member   Join Date: May 2009 Posts: 8 KCl and simultaneus equations I am struggling as usual with quite a confusing circuit i need to find i1 i2 and i3 in this circuit using kirchoffs laws R1=.5 ohm R2=1 ohm R3=1ohm R4=.5ohm R5=1ohm i know i need 3 loops loop 1 is V1...ABCD....V1 loop 2 is V1...ACD.....V1 Loop 3 is V1....ABD....V1 i have worked out loop1 to be I1R1-I3R5-(I2+I3)R4 = 1V but the other loops look wrong and then i cant seem to use simultaneus equations effectively. Any help much appreciated Attached Thumbnails
Jun 4th 2009, 05:56 PM   #2

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 Originally Posted by tommoturbo I am struggling as usual with quite a confusing circuit i need to find i1 i2 and i3 in this circuit using kirchoffs laws R1=.5 ohm R2=1 ohm R3=1ohm R4=.5ohm R5=1ohm i know i need 3 loops loop 1 is V1...ABCD....V1 loop 2 is V1...ACD.....V1 Loop 3 is V1....ABD....V1 i have worked out loop1 to be I1R1-I3R5-(I2+I3)R4 = 1V but the other loops look wrong and then i cant seem to use simultaneus equations effectively. Any help much appreciated
I've made some changes to your diagram. You only need three of the six currents on the diagram, but I suspect you'll have to find them anyway.

So, first let's talk about the junction rule.
At point A we have $\displaystyle I_0 = I_1 + I_2$
At point B we have $\displaystyle I_1 = I_3 + I_4$
At point C we have $\displaystyle I_2 + I_3 = I_5$
At point D we have $\displaystyle I_5 + I_4 = I_0$

Four equations in six unknowns. We need two more equations. Let's use your ABCD loop:
$\displaystyle -I_1R_1 - I_3R_5 - I_5R_4 + 1 = 0$

And let's pick the ABDC path:
$\displaystyle -I_1R_1 -I_4R_3 + I_5R_4+I_2R_2 = 0$

Give solving that system a try and see what you can come up with. If you need more help, simply ask.

-Dan
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 Jun 4th 2009, 09:31 PM #3 Junior Member   Join Date: May 2009 Posts: 8 Thanks Dan Will give it a go ian

 Tags equations, kcl, simultaneus

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