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$\text{We were doing problems on Kirchoff's Laws in my class. The problem :}$

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My Professor told that from $B_1$ current $i_1$ is flowing which splits into $i_2,i_3⇒i_1=i_2+i_3$. Then he used Kirchoff's Laws in loops to get $i_1,i_2,i_3.$ But why did taking only $1$ current ie from $B_1$ worked? Similarly shouldn't other currents flow from $B_2,B_3$? Can someone explain?

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    $\begingroup$ Welcome to PhysicsSE. Sometimes we ask users to clarify their questions, you can do that by editing your post. I would like to know, what do you mean by "why did taking only 1 current ie from 𝐵1 worked?" ? $\endgroup$
    – Mauricio
    Feb 14, 2022 at 9:33

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You have 3 unknown variables : $i_1,i_2,i_3$ which are the currents that flow through each resistor. $i_1$ is not the current that results from $B_1$ being active. It is the current that passes through the resistor $R_1$. So by using two voltage laws (2 loops) and one current law you have 3 equations for 3 unknowns and you solve the system for $i_1,i_2,i_3$.

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