How to find Thevenin’s Resistance ?

We have three methods to find Thevenin’s resistance which are classified into two cases.

(1) When circuit contains only independent sources :-

To find R_Th , open circuit the load resistance. Now replace all independent voltage sources by short circuit (sc) and  all independent current sources by open circuit (oc). 

You will be left with a circuit containing resistances only and thevenin  resistance can be found out easily looking through the open circuited load terminals.

Example :- The problem circuit is shown in first image and its equivalent resistance circuit after applying above method is shown in second figure.

From the second figure,

(2) When circuit contains dependent sources in addition to or in  absense   of independent sources :-

For such circuits R_Th can be found out by two methods.

Method-1 :- Open circuit load resistance. 

Replace all independent voltage sources by sc and all independent current sources by oc , keeping dependent sources as it is. 

Find voltage across open circuited load terminals by conventional  analysis like Kirchoff’s current law , Kirchoff’s voltage law etc.

Upto this point you will have Thevenin’s voltage V_Th . 

Now short circuit the load terminals and find short circuited current. Let it be  I_sc

Now, Thevenin’s resistance can be found out as     R_Th = V_Th / I_sc

Solved Example :-  Find R_Th looking through  5Ω resistor.

      

      

Remove 5Ω resistor. No current will flow through 1Ω resistor so that dependent current source becomes zero. No current flows in any part of the circuit giving   

V_Th = 6V .

       

Next find I_sc . Short open circuited load terminals. Let short circuited current be I_sc . The  dependent current source becomes 0.5 I_sc  .

      

       

Apply Kirchoff’s voltage law in outer loop,

6 - 2 (1.5 I_sc) - I_sc = 0

Giving   I_sc = 1.5 A

      

Method-2 :- 

Remove load resistance and apply a dc driving voltage V_dc at the open circuited terminals. 

Replace all independent voltage sources by sc and all independent current sources by oc , keeping dependent sources as it is. 

A dc driving current I_dc will flow to the circuit from the load terminals due to application of V_dc .

Solved Example :- Find R_Th across open circuited terminals.

Apply a dc source V_dc across the open-circuited terminals. Let current supplied by the source be I_dc . 

Replace all independent voltage sources by sc and all independent current sources by oc , keeping dependent sources as it is. 

       

       

Applying KCL at node x :-

  

Closely related concepts :-
   (1) Thevenin’s Theorem explained by solved example