Currents and Voltages in a simple electrical circuit can be found by using Ohm's law. For a complex electrical circuit , kirchhoff's laws are used to find the currents and Voltages in different parts of the circuit.
Kirchhoff's First Law or Rule ( The Junction Law or Kirchhoff's Current Law ) :
It states that the sum of all the current entering any point ( or Junction or node or branch point ) must be equal to the sum of all current leaving that point.
Or
The algebraic sum of all the currents meeting at a point in a closed electrical circuit is zero.
\[\sum I = 0\]
\[I_{1}+I_{3}=I_{2}+I_{4}+I_{5}\]\[I_{1}+I_{3}+(-I_{2})+(-I_{4})+(-I_{5}) = 0\]\[I_{1}+I_{3}-I_{2}-I_{4}-I_{5} = 0\]