Monday 15 October 2012

Norton’s Theorem Statement And Norton’s Theorem solved Method

Norton’s Theorem Statement And Norton’s Theorem solved Method


Consider a circuit,

The solution of the given problem is not done by the actual given circuit, we have to find-out the value of any unknown (i.e, V,I or P) through any resistance as per question is said we design a new circuit and the circuit is known as “Norton’s equivalent circuit”.

Norton’s equivalent circuit has containing one current source in parallel with two resistances ‘RL’ & ‘RN’. As shown in fig. below:-

Here,
IN/IS.C = Norton’s equivalent current (“It is that Current from required unknown through any resistance is removed and short-circuited.”)

RN =Norton’s equivalent resistance (“It is that equivalent resistance from required unknown through any resistance is removed”) &

RL =Called “Load-Resistance” (The resistance in which unknown is required).

Method Of Solving “Norton’s Theorem”:-

For finding RL: - Suppose that from above given circuit, asked to find-out the value of current through ‘R4’ resistance. Then the resistance along which any unknown is asked to find-out that resistance becomes “Load-resistance”.
Here, RL=R4

For finding RN: - For finding RN, Just find-out equivalent b/w removed load-resistance. Like as:-
Step 1st:- Firstly removed the load-resistance from the given circuit

Step 2nd:- Deactivating all the energy sources of the fig. Step 1st:-

Step 3rd:- Now, RN is actually the equivalent resistance b/w that two ends from load-resistance are removed of fig. Step 2nd:-
For finding IN/IS.C: - For finding IN/IS.C in given circuit diagram, we have to follow the given steps:-
Step 1st:- Removed load-resistance from the given problem circuit.

Step 2nd:- Short-circuit the open part from where the load-resistance is removed.

The current flow through short-circuited path is the required current IN/IS.C  which we can find-out any of the method we have studied earlier in this website.(Easy to use Mesh-analysis) 
                            
Now, the Norton’s equivalent circuit is,

By using current division rule, we can easily find-out the value of IR4 Ω in the given problem.

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