2.9: Norton's Theorem

2.9: Norton's Theorem

Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (Ⅰ_N) in parallel with a resistor (R_N). Here, Ⅰ_N represents the short-circuit current flowing through the terminals, and R_N stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the one depicted in Figure (b).

Figure (a)

Figure (b)

The determination of Norton's resistance involves the process of setting all independent sources within the circuit to zero. The resulting value represents Norton's resistance, which is essential for the theorem's application. To calculate Norton's current, one must restore all sources to their original configurations and then ascertain the short-circuit current between the marked terminals. Replacing the network with the Norton equivalent circuit and reconnecting the load resistor is necessary to complete the transformation. To establish either the Thévenin or Norton equivalent circuit, one must have knowledge of the open-circuit voltage, short-circuit current, and input or equivalent resistance. These parameters serve as crucial inputs for these circuit transformations. The close relationship between Norton's and Thévenin's theorems given by the following relations,

coupled with the principles of Ohm's law, provides valuable tools for resolving intricate electrical circuits.