Kirchhoff's Laws

Kirchhoff's Laws are Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL).

Kirchhoff's Current Law (KCL): all the current flowing into a node must equal the current flowing out of that node.

For any simple series circuit, the current must be the same everywhere.

Kirchhoff's Voltage Law (KVL): the algebraic sum of the all the voltage drops in a circuit equal zero.

Example: The circuit is a battery with voltage V_s and 2 resistors in series with voltage drops -V₁ and -V₂. The two voltage drops must have the same magnitude of the battery voltage, but the opposite sign.

KVL can be tricky to understand if you are already using the concept of a "common" or "ground" voltage. In that case, you would read all voltages with respect to a common node in the circuit, and for a single battery circuit you would not get positive and negative voltages. The above description implies that there is no "common" node. Each voltage is measured across the individual components. To get the correct algebraic sign, you have to be careful as to which side of the component gets the "red"/positive lead, and which side gets the "black"/negative lead. If the components were laid out in a circle, connected in series, you would keep one lead (let's say the black lead) in your left hand and the other lead in your right hand and go around clockwise placing the leads across each component. This would ensure you would get the correct algebraic signs to observe KVL.