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Thevenin theorem and Norton theorem | thevenin vs Norton

This page covers basic description of thevenin theorem and Norton theorem. It mentions step by step guide to solve the network using thevenin theorem and Norton theorem.

Both of these are used widely as network theorems. It is useful where is is needed to find current through or voltage across any element of a network without solving any complex equations.

Thevenin Theorem

Thevenin theorem

As per thevenin theorem, "any two terminal bilateral linear DC circuit can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

Let us take example as mentioned in figure-1 and derive IL using thevenin theorem.
1. Find Voc ,
First rL is removed and then Voc is found using following equation.
⇒Voc = I*r3 = [ Vs/(r1+r3) ]* r3

2. Find Rth
Determine thevenin resistance of the circuit by replacing voltage source by short circuit. If current source is present in the network, replace it by open circuit.

3. Find IL as mentioned in thevenin equivalent circuit shown in Fig.1(d)
⇒IL = [ Voc/(RTh + rL ) ]

Thevenin network ≡ equivalent voltage source in series with internal resistance.

Norton Theorem

Norton theorem

Norton theorem is converse of the Thevenin theorem mentioned above. It consists of equivalent current source instead of equivalent voltage source as used in thevenin theorem.

The similarity between the two is that calculation of internal resistance of the network is same.
Norton network ≡ equivalent current source in parallel with internal resistance

Following steps are used to determine Norton equivalent circuit.
1. Find ISC
In order to determine ISC, replace rL by short circuit.
⇒ i = Vs/[ r1 + {(r2*r3)/(r2+r3)} ] and ISC = i *[ r3/(r3+r2)]


2. Find RTH
Now remove the short circuit and deactivate independent source to determine Rint as follows
⇒ Rint = r2 + [(r1*r3)/(r1+r3)]

3. As per Norton theorem, the equivalent source circuit would contain current source in parallel with internal resistance. Current source will be short circuited current across shorted terminals of the load resistor.
⇒ IL = iSC * [ Rint/Rint + rL ]

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