Whose law states that at a junction in an electric circuit, the sum of the currents flowing into the junction is equal to the sum of the currents flowing out of the junction?

Gustav Robert Kirchhoff

The correct answer is option 4. Gustav Robert Kirchhoff.

Kirchhoff's current law, often abbreviated as KCL, is a fundamental principle in electrical engineering and circuit analysis. It is based on the principle of conservation of electric charge.

In an electrical circuit, a node refers to a point where two or more circuit elements meet. Kirchhoff's current law states that the total current entering a node must be equal to the total current leaving the node, considering the algebraic sign convention.

Mathematically, if \( I_1, I_2, \ldots, I_n \) represent the currents entering the node, and \( I'_1, I'_2, \ldots, I'_m \) represent the currents leaving the node, then according to Kirchhoff's current law:

\[ I_1 + I_2 + \ldots + I_n = I'_1 + I'_2 + \ldots + I'_m \]

This law is a consequence of the conservation of electric charge, which states that electric charge cannot be created or destroyed; therefore, the total current flowing into a node must equal the total current flowing out of it.

Kirchhoff's current law is invaluable in analyzing complex electrical circuits, allowing engineers to determine unknown currents and voltages at various points within the circuit.