Norton's Theorem is a fundamental concept in circuit theory, specifically in the analysis of linear electrical circuits. It's named after Edwin Norton and is closely related to Thevenin's Theorem. Norton's Theorem states that any linear, bilateral electric network can be replaced by an equivalent current source and a parallel resistance.
Here's a breakdown of Norton's Theorem and its key components:
Original Circuit: Consider a linear electric network with multiple components such as resistors, voltage sources, current sources, and so on.
Equivalent Current Source (Norton Current): Norton's Theorem allows us to replace the entire original network with a single current source in parallel with a resistance. The equivalent current source is known as the "Norton current" (I_N), and it represents the total current that would flow through a short circuit across the terminals of the original network.
Equivalent Resistance (Norton Resistance): The parallel resistance associated with the Norton equivalent represents the input or terminal resistance of the original network as seen from the terminals where the Norton current source is connected. This resistance is termed the "Norton resistance" (R_N).
Mathematically, the Norton equivalent circuit can be represented as follows:
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I_N = Norton Current
R_N = Norton Resistance
Equivalent Norton Circuit:
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I_N
----/\/\/\---- Load
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R_N
To find the Norton current (I_N) and the Norton resistance (R_N), you typically follow these steps:
Find the Short-Circuit Current (I_SC): Calculate the current that flows through the short circuit terminals (where the original network is connected) when all voltage sources are replaced by short circuits and all current sources are replaced by open circuits.
Find the Norton Current (I_N): The Norton current (I_N) is the same as the short-circuit current (I_SC) calculated in step 1.
Find the Norton Resistance (R_N): To find the Norton resistance, remove all the sources from the original network and calculate the resistance seen between the terminals where the sources were connected.
Norton's Theorem simplifies circuit analysis by reducing complex circuits to simpler forms, making it easier to perform calculations and analyze the behavior of the circuit under different conditions. It's particularly useful when dealing with networks that have multiple sources and resistors.