Kirchhoff's circuit laws — balance in a circuit

What just happened?

You added current to one of the incoming branches, and the current leaving the node rose by exactly the same amount. Charge cannot accumulate at a point — whatever flows in must flow out.

Kirchhoff's first law (current / junction):

— the sum of currents flowing into a node equals the sum of currents flowing out. This is a direct consequence of charge conservation: nothing is lost or created at the node.

Zero-balance form:

— if we assign a "+" sign to incoming currents and "−" to outgoing ones, their sum at the node is zero. This is the same condition written differently.

And Kirchhoff's second law?

In any loop of the circuit the sum of voltages is zero: $\sum U = 0$. This in turn follows from energy conservation — walking around the loop back to the start, we return to the same potential.

Why you need this for the exam:

The first law (junctions) plus the second law (loops) let you write equations for any branched circuit. The trick: mark the current directions, write the balance at every node and the sum of voltages in every loop — the rest is solving the system of equations.

Remember: at a node, as much current flows in as flows out (ΣI = 0 — charge conservation); in a loop the sum of voltages is zero (ΣU = 0 — energy conservation). These are the two pillars of circuit analysis.