# Why does taking one current from any cell work?

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

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?

• 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?" ? Feb 14, 2022 at 9:33

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 $$i_1,i_2,i_3$$.