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Published byJavon Frickey Modified about 1 year ago

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Norton’s Theorem Statement: Norton’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources and resistors can be replaced by a simple equivalent circuit containing a single current source in parallel with a resistor”.

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Norton’s Equivalent Circuit. loadSource Here, I N = I sc (short circuit current) R N = R th = equivalent R (total R) in the circuit RL = load resistance of network through which the current or across which the voltage is the to be calculated

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Steps to solve circuit using Norton’s Theorem Calculation of I N : 1.First short circuiting the load resistance 2.finding the short circuit current between the load terminals - remember that the short circuit will effectively remove all components in parallel with it. Calculation of R N : 1.Calculate the Norton Resistance R N by a. Marking the terminals as R N where the load was removed from and setting all sources to zero (voltage sources are replaced by a short circuit and current sources by an open circuit) b.Finding the resistance between the two load terminals.This ll be the same as R th 2. Draw the Norton’s equivalent circuit and return the load for analysis.

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Example 1. Determine the current through R L using Norton’s theorem

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i1i1 i2i2 i3i3

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Determination of R N :

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Step 3: Calculate R N

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Step 4: Draw the equivalent circuit

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Solution Step 1: Source transformation (The 25V voltage source is converted to a 5 A current source.) Example 2 Derive the Norton equivalent circuit of the given circuit

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Step 3: Source transformation (combined serial resistance to produce the Thevenin equivalent circuit.) Step 2: Combination of parallel source and parallel resistance

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Step 4: Source transformation (To produce the Norton equivalent circuit. The current source is 4A (I = V/R = 32 V/8 ) 8 a b 4 A Norton’s Equivalent Circuit

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Example 3 Refer to the Figure, find the Thevenin equivalent circuit. Solution In order to find the Thevenin equivalent circuit for the circuit shown in Figure, calculate the open circuit voltage, vab. Note that when the a, b terminals are open, there is no current flow to 4Ω resistor. Therefore, the voltage vab is the same as the voltage across the 3A current source, labeled v 1. To find the voltage v 1, solve the equations for the singular node voltage. By choosing the bottom right node as the reference node,

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By solving the equation, v1 = 32 V. Therefore, the Thevenin voltage Vth for the circuit is 32 V. Rth = (20II5)+4=8 ohms Thevenin Equivalent Circuit

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Example 4. Determine the current through R 2 using Norton’s theorem

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Determination of I N :

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Determination of R N : RNRN

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Norton’s equivalent circuit:.8 Using current division rule, current through R 2 is

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Thevenin’s and Norton’s Theorems In many cases we are not interested in how a whole circuit operates but only how one or two components react when connected to a particular circuit. Thevenin’s Theorem allows us to reduce a circuit to a single voltage source with a series resistor. Norton’s Theorem allows us to reduce a circuit to a single current source with a parallel resistor. Once this reduction is made then the one or two components we are interested in can be added to see what voltage would be across them, how much current would be drawn etc.

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