Kirchhoff's Laws dictate how electricity moves within a circuit

Current Law

Kirchhoff's Current Law states that the current going into a node or component must be the same as the current going out of the node or component

\sum 𝐼 𝑖 𝑛 = \sum 𝐼 𝑜 𝑢 𝑡

Consider these two scenarios

In both cases the total current into the system equals the total current out of the system

Voltage Law

Kirchhoff's Voltage Law states that all voltage rises must be accompanied by voltage drops

\sum 𝑉 𝑎 𝑑 𝑑 = \sum 𝑉 𝑑 𝑟 𝑜 𝑝

And therefore the sum of all voltage across a circuit must sum up to zero

Consider this Loop containing three components

Since the total rises must equal the total drops $𝑉 𝐴 = 𝑉 𝐵 + 𝑉 𝐶$ , therefore $𝑉 𝐶 = 2 𝑉$

Loops within Loops

The equivalent KVL of a bigger loop is the sum of all independent loops within it