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Finding Current in a Circuit

  • #1

Homework Statement


Find the Loop currents that are shown in the network of the figure below.

Homework Equations


V=IR

The Attempt at a Solution


I know that I need to create 3 equations since there are three unknown currents and then solve for them so here is what I got.
1) [tex] 10V-5I_1-2I_1=0 [/tex]
2) [tex] 10V-5I_3-3I_3-20V-4I_3+4I_2=0 [/tex]
3) [tex] 4I_2-4I_3+2I_2=0 [/tex]

When I solve for the currents I get
[tex] I_1=1.43A [/tex]
[tex]I_2=-0.71A [/tex]
[tex]I_3=-1.07A [/tex]

While the correct answers should be 3.55A, -1.98A, -2.98A. I suspect that my equations are incorrect but I can't come up with any equations that give me the right answer or make any sense.

Thanks,
 

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Answers and Replies

  • #2
gneill
Mentor
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As you 'traverse' each resistive component in a given loop, you need to take into account all the currents flowing through that component. So, for example, the voltage drop across your 5Ω resistor is (I1 + I3)*5Ω.
 
  • #3
Yea that was the concept I couldn't fully understand... I get it now.
In case anyone else is interested here are the equations that actually work:
1) [tex] 10V-5I_1-2I_1-5I_3=0 [/tex]
2) [tex] 10V -5I_1-5I_3-3I_3-20V-4I_3+4I_2=0 [/tex]
3) [tex] 4I_2-4I_3+2I_2=0 [/tex]

gneill You've been a great help as usual! Thanks!
 

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