Checking Equations: Are They Correct?

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geft
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Are my equations correct?

[tex]I_3=I_1+I_2[/tex]
[tex]V_{S1}=I_1(R_1+jwL_1+jwL_3+R3)-I_2(jwL_3+R_3+M)[/tex]
[tex]-V_{S2}=I_2(R_3+jwL_3+jwL_2+R2)-I_1(jwL_3+R_3+M)[/tex]
 
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Your loop equations look okay provided that your I2 is not the same as the I2 indicated on the diagram (they are assumed to be flowing in opposite directions).
 
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Ah, my bad for not posting the complete question. For the first part, V2 is assumed 0, so they should be okay. Thanks!