- #1
Edge Of Pain
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Homework Statement
This is quite an easy problem but I'm not sure if I set up my equations correctly, and I want confirmation.
We are given the following circuit:
And our task is to determine the loop currents [itex] i_{1}, i_{2}, i_{3}, i_{4} [/itex].
Homework Equations
Kirchhoff's first law: sum of currents entering and leaving a loop = 0.
Kirchhoff's second law: sum of electromotive forces = sum of potential difference of loop.
Ohm's law: V = IR.
The Attempt at a Solution
Just apply Kirchoff's laws and Ohm's laws to get the following:
loop 1:
[itex] 50(i_{1} - i_{2}) + 30(i_{1} - i_{3}) = 120V [/itex]
loop 2:
[itex] 50(i_{2} - i_{1}) + 15i_{2} + 10(i_{2} - i_{3}) + 25(i_{2} - i_{4}) = 120V [/itex]
loop 3:
[itex] 30(i_{3} - i_{1}) + 10(i_{3} - i_{2}) + 20(i_{3} - i_{4}) + 5i_{3} = 120V [/itex]
loop 4:
[itex] 25(i_{4} - i_{2}) + 10i_{4} + 30i_{4} + 15i_{4} + 20(i_{4} - i_{3}) = 120V [/itex]
I'm not concerned about finding the numerical values, I'm just wondering if I've set these equations up correctly. Are some of these supposed to be -120 volts on the right hand side? If so, how do I determine that?