KCL, KVL and types of sources

Kirchhoff's laws

KCL (current law): the algebraic sum of the currents meeting at a node is zero. Equivalently, current entering a node equals current leaving it: $\sum I=0$. It follows from conservation of charge.

KVL (voltage law): the algebraic sum of all voltages (sources and drops) around any closed loop is zero: $\sum V=0$. It follows from conservation of energy.

Voltage and current sources

An ideal voltage source keeps a fixed terminal voltage whatever the load current; its internal resistance is zero. A practical voltage source is an ideal source $E$ in series with an internal resistance $r$, so $V=E-Ir$ and the terminal voltage falls with load.

An ideal current source supplies a fixed current whatever the load voltage; its internal resistance is infinite. A practical current source is an ideal source $I_s$ in parallel with an internal resistance $r$.

Source conversion. A practical voltage source $E$ with series $r$ is equivalent to a current source $I_s=E/r$ with the same $r$ in parallel, which simplifies network analysis.