Kirchhoff’s Law
Kirchoff’s Laws are two fundamental rules in electrical circuit analysis. They help find unknown currents and volrages and resistance values in complex circuits.
Kirchhoff’s Current Law (KCL) - Node Rule
Definition: The algebraic sum of currents entering a junction equals to the sum of currents leaving the junction.
\begin{equation} \begin{aligned} \underbrace{\sum_{j}I_j}_\text{current entering} = \underbrace{\sum_{j}I_j}_\text{current leaving} \end{aligned} \end{equation}
Kirchhoff’s Voltage Law (KVL) - Branch Rule
Definition: The algebraic sum of all voltage rises and drops around any closed loop is zero.
\begin{equation} \begin{aligned} \sum_{j}V_j = 0 \; {around \; a \; loop} \end{aligned} \end{equation}
Points to Remember
Two voltage sources connected in series can be combined into a single voltage source. If their polarities are aligned, the resulting voltage is simply the sum of both sources. If the polarities oppose each other, the resulting voltage is the difference between the two.
Similarly, current sources connected in parallel can be combined into one equivalent current source. When both currents flow in the same direction, the equivalent current is the sum of the two. If they flow in opposite directions, the equivalent current is the difference between them.