Kirchoff’s Laws

To analyze circuits, we want to find the potential difference and the current in each circuit component. To do so, we must understand two very important laws.

Kirchhoff’s Current Law (KCL)

Because charge and current are conserved, the total current into the node must equal the total current leaving the node. That is,

$\sum I_{in}=\sum I_{out}$

Based on Law of Conservation of Charge.

Another way to state it is that the algebraic sum of all currents at any node is zero, i.e.
$$\sum_{n}{i_n} = 0$$
*Convention*: Currents entering the node are taken as **negative**, and currents leaving the node are taken as **positive**.

See Nodal Analysis.

Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s voltage law states that the algebraic sum of the potential differences around any loop is zero.

$\Delta V_{loop}=0$

The algebraic sum of all voltages around any loop is zero, i.e.
$$\sum_{n}{v_n} = 0$$
*Convention*: Voltage drop (+ to -) is written as **positive**, while a voltage rise (- to +) is written as **negative**.

Strategy Using Kirchhoff’s Voltage Law

1. Draw a circuit diagram
2. Assign a direction to the current
3. Travel around the loop.

Practice lots! The theory can only helpful you so much.