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

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 I_L using thevenin theorem.
1. Find V_oc ,
First r_L is removed and then V_oc is found using following equation.
⇒V_oc = I*r3 = [ Vs/(r1+r3) ]* r3

2. Find R_th
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 I_L as mentioned in thevenin equivalent circuit shown in Fig.1(d)
⇒I_L = [ V_oc/(R_Th + r_L ) ]

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

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 I_SC
In order to determine I_SC, replace r_L by short circuit.
⇒ i = Vs/[ r1 + {(r2*r3)/(r2+r3)} ] and I_SC = i *[ r3/(r3+r2)]


2. Find R_TH
Now remove the short circuit and deactivate independent source to determine R_int as follows
⇒ R_int = 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.
⇒ I_L = i_SC * [ R_int/R_int + r_L ]

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