2.9:
Norton’s Theorem
Norton's theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a single current source in parallel with a resistor.
To implement Norton's theorem, remove the load resistor from the two load terminals: the remaining network will be substituted by the Norton equivalent circuit as seen from these terminals.
Norton's resistance can be determined by setting all independent sources to zero. The equivalent or input resistance between the terminals is Norton's resistance.
To find Norton's current, return all sources to their original positions. Then, calculate Norton's current by finding the short-circuit current between the marked terminals.
Finally, replace the network with the Norton equivalent circuit and connect the load resistor again.
The source transformation technique can be used to convert between Norton and Thévenin equivalent circuits.
Open circuit voltage, short circuit current, and input or equivalent resistance must be known to determine the Thevenin or Norton equivalent circuit.
The close relationship between Norton's and Thévenin's theorems and Ohm's law helps solve complex electrical circuits.
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 (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN 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.