Kirchoff's 1st Law
A conservation of stuff law
Kirchoff's first law says that charges can't just disappear and they can't appear from nowhere. So at every junction in a circuit the current going in must equal the current going out.
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This law is often used in the junctions at parallel circuits but it also implies that the current must be the same all the way round a series circuit.
A caveat
Kirchoff's first law doesn't suggest any of the deeper physics of a circuit. In particular it doesn't say that current splits at junctions, simply that the current into a junction must equal the current coming out.