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Verification of Norton’s theorem
Apparatus
Breadboard, Batteries or DC regulated power supply, Resistors, Digital multimeter, Connecting wires, Alligator clips, Computer and Multisim software for simulation.
Theory
Norton’s theorem is used to convert a complex linear network into a simple network consists of a current source in parallel with a resistor and load resistor.
Statement
- “Any linear circuit containing several energy sources and resistances can be replaced by a single constant current source in parallel with a resistor”.
- it is possible to simplify any complex electrical circuit, to an equivalent circuit with just a single constant current source in parallel with a resistance (or impedance) connected to a load.
Procedure to convert the given network into Norton’s equivalent circuit
- Find the Norton source current by removing the load resistor R_{L} from the original circuit and calculating the current I_{N} through a short (wire).
- Find the Thevenin’s/ Norton’s resistance (R_{TH }or R_{N}) by removing all power sources from the original circuit (voltage sources shorted and current sources open) and calculating total resistance between open connection points.
- Draw the Norton’s equivalent circuit, with the Norton current source (I_{N}) in parallel with the Norton resistance and load resistance.
4. Find voltage or current for the load resistor.
Circuit Diagram
[Preferably chose R1= 2KΩ, R2= 450Ω, R3= 1kΩ and RL=300Ω, V1= 12V and V2= 9V.]
Procedure
- Connect the circuit as shown in the figure 3.
- Measure and note down the current flowing through load resistor R_{L}.
- Remove the load resistor R_{L} from the circuit and short circuit the terminals A and B, shown in figure 4. Measure the current flowing through shorted terminal. This is current I_{N}.
4. Replace the sources with their internal resistances (with removed R_{L}) as shown in figure 5. Measure and note down the equivalent resistance across the terminals from which the resistor R_{L} is removed (between A and B). This is resistor R_{TH} or R_{N}. (Note that Thevenin’s equivalent resistance and Norton’s equivalent resistance is same.)
5. Convert the given network into Norton’s equivalent network and make the connection as shown in the figure 6.
Alternate circuit arrangement for Norton’s equivalent circuit.
6. Measure and note down the current flowing through resistor R_{L}.
Note: If current source is not available in the laboratory, it can be built by using source transformation. In Norton’s equivalent circuit, the current source I_{N} and a parallel resistance can be converted into voltage source in series with same resistance.
Where, voltage source V_{S}=I_{N}.R
In fact, if we replace above combination i.e. a voltage source and a series resistance then the Norton’s equivalent circuit get converted into Thevenin’s equivalent circuit. Hence Thevenin’s equivalent circuit and Norton’s equivalent circuit is dual of each other.
Precautions
- All the connection should be tight.
- Ammeter must be connected in series while voltmeter must be connected in parallel to the components (resistors).
- Before circuit connection working condition of all the components must be checked.
- The electrical current should not flow the circuit for long time, otherwise its temperature will increase and the result will be affected.
Observation table
Sr. No. | R_{TH} | I_{N} | I_{L} | |
1. | Theoretical | |||
2. | Practical |
Calculations
R_{1}=_____ Ω
R_{2}=_____ Ω
R_{3}=_____ Ω
V_{1 }=_____V
V_{2} =_____V
[calculate I_{L} from figure 3]
[calculate I_{N} from figure 4]
[calculate R_{TH} from figure 5]
The current flowing through load resistor R_{L }in Norton’s equivalent circuit (Fig. 6),
Result
Calculated value of current flowing through load resistor R_{L }in circuit (Fig. 3),
I_{L}= ______A.
Measured value of current flowing through R_{L} in original complex circuit (Fig. 3),
I_{L}= ______A.
Calculated value of current flowing through R_{L} in Norton’s equivalent circuit (Fig. 6 or 7),
I_{L}= ______A.
Measured value of current flowing through R_{L} in Norton’s equivalent circuit (Fig. 6 or 7),
I_{L}= ______A.
Conclusion
As the current flowing through the complex linear circuit and Norton’s equivalent circuit is same/nearly same. It can be determined that any linear network can be converted into Norton’s equivalent network.
That is “Any linear circuit containing several voltages and resistances can be replaced by just one single current source in parallel with a single resistance connected across the load”. Hence Norton’s theorem is verified.
Video Tutorial on Norton's Theorem
Reference Video Tutorial for calculation of Verification of Nortons Theorem
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