Question

How do you determine a system of linear equations needed to solve for the current on wires in a circuit/how do you solve for these system of equations?

Answer 1

We use the Kirchhoff's junction rule to relate the currents in the circuits and make the linear equations using the Kirchoff's loop rule.

Number of unknowns and always equals the number of equation. Solving these we can always find the respective currents in the circuit.

Kirchhoff's junction rule is an application of the principle of conservation of electric charge: current is flow of charge per time, and if current is constant, that which flows into a point in a circuit must equal that which flows out of it.

Kirchhoff's Loop Rule states that the sum of the voltage differences around the loop must be equal to zero.

Note: its always better to use the junction rule before applying loop rule.