Norton’s Theorem Statement: Norton’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources.

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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”.

Norton’s Equivalent Circuit
. Source load Here, IN= Isc (short circuit current) RN = Rth = 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

Steps to solve circuit using Norton’s Theorem
Calculation of IN : First short circuiting the load resistance 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 RN : Calculate the Norton Resistance RN by Marking the terminals as RN 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) Finding the resistance between the two load terminals.This ll be the same as Rth Draw the Norton’s equivalent circuit and return the load for analysis.

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

i3 i1 i2

Determination of RN:

Step 3: Calculate RN

Step 4: Draw the equivalent circuit

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

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

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

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 v1. To find the voltage v1, solve the equations for the singular node voltage. By choosing the bottom right node as the reference node,

By solving the equation, v1 = 32 V
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

Example 4. Determine the current through R2 using Norton’s theorem

Determination of IN :

Determination of RN : RN

Norton’s equivalent circuit:
.8 Using current division rule, current through R2 is

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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