Kirchhoff's current law is based on the conservation of:

Kirchhoff's Current Law (KCL) is the statement, for any junction (node) in a circuit, that the algebraic sum of the currents meeting there is zero -- equivalently, total current in equals total current out. It is one instance of a general conservation principle applied to the standard lumped-circuit model: a node itself is treated as a point with no independent capacity to store charge (any real charge storage at a junction is modelled separately as a capacitive circuit element), so an ideal node cannot let a conserved quantity build up inside it.

The conserved quantity relevant to a circuit junction is electric charge. Current is defined as the rate of flow of charge (I = dQ/dt); charge conservation says the net rate of charge buildup anywhere equals the net current flowing in. For an idealised node with no charge storage of its own, that net buildup is zero by definition, so the currents at the node must sum to zero -- this is exactly KCL, which is why the law is described as based on conservation of charge.

• Momentum conservation governs mechanical interactions such as collisions and projectile motion -- a property of moving bodies. It has no bearing on the quantity that flows through and balances out at an electrical junction, so it cannot be what this circuit law rests on.

• The electrons carrying the current do have mass, but KCL is not a mass-balance statement -- it holds regardless of how much mass the charge carriers have, because it tracks charge (via current), not mass. Mass conservation is therefore not the principle this law encodes.

As a further check: writing KCL as (sum of incoming currents) minus (sum of outgoing currents) equals zero is algebraically identical to saying the ideal node's rate of charge accumulation is zero at every instant -- the direct statement of charge conservation applied to a lumped node.