What Are Kirchhoff's Laws? (Current and Voltage Law)

Kirchhoff's laws are the fundamental rules for solving the currents and voltages in an electrical circuit. There are two laws: the current law (KCL) and the voltage law (KVL). Together with Ohm's law, they're the key to analyzing complex circuits.

Kirchhoff's Current Law (KCL)

At a node (a point where several wires meet), the sum of the currents entering equals the sum of the currents leaving. That is, charge doesn't pile up in the circuit. For example, if 3 A enters a node and 1 A leaves through one branch, then 2 A must leave through the other branch.

Kirchhoff's Voltage Law (KVL)

Around a closed loop, the sum of the voltage rises and drops is zero. The voltage the source supplies equals the sum of the voltage drops across the components in that loop.

Worked Example (KVL)

There are two resistors in series across a 9 V battery, and 4 V drops across the first. By KVL the total around the loop must be zero; so the voltage across the second resistor is 9 − 4 = 5 V. This logic is the basis of series and parallel calculations.

Where Is It Useful?

Kirchhoff's laws are used to solve multi-source or multi-branch circuits where Ohm's law alone isn't enough. The node-voltage and mesh-current methods are based entirely on these two laws.

Common Mistakes

• Mixing up signs (direction): in KVL, voltage rises (+) and drops (−) must be taken in a consistent direction.
• Choosing the node wrong: in KCL, points connected to the same wire count as a single node.
• Forgetting Ohm's law: Kirchhoff balances the currents/voltages; you still need V = I × R for component values.