How is the law of nodes skillfully applied?

Law that clarifies the bounding relationship between the individual currents flowing into and out of a node in a lumped-parameter circuit, and between the voltages along the segments of the circuit.Proposed in 1845 by the German physicist G.R. Kirchhoff. A lumped-parameter circuit is a circuit in which the maximum linear dimension of the circuit itself is much smaller than the wavelength of the current or voltage in the circuit, and vice versa for a distributed-parameter circuit. Kirchhoff's laws include the current law and the voltage law.

Kirchhoff's current law (KCL) The algebraic sum of all currents flowing out of any node in any aggregate parametric circuit at any instant is constant zero, i.e., with respect to the direction of reference, the currents flowing out of the node take a positive sign in Eq. and the currents flowing into the node take a negative sign. Kirchhoff's current law is the embodiment of the law of conservation of charge in electric circuits.

Kirchhoff's voltage law (KVL) Any loop in any collective parameter circuit, at any instant of time the algebraic sum of the voltages along the segments of this loop is constant to zero, that is, when the reference direction of the voltage is the same as the direction of the loop's winding, the voltage takes a positive sign in Eq. Otherwise, it takes a negative sign. Kirchhoff's voltage law is the law of conservation of energy in the circuit.