Different Methods of Finding Thevenin Resistance

In this article, we will discuss the different methods of finding Thevenin’s resistance (R_TH).

Case 1: For circuits containing independent sources only

When an electric circuit contains independent sources only, then the most common method of determining Thevenin’s resistance (R_TH) is explained as follows:

Step I – Remove the load resistance.

Step II – Deactivate all the independent current and voltage sources in the circuit by their internal resistances. For an independent current source, deactivate it by removing the current generator. For an independent voltage source, deactivate it by short-circuiting the voltage generator.

Step III – Determine the internal resistance of the network by looking through the open-circuited load terminals. This will be Thevenin’s resistance (R_TH) of the circuit.

Case 2: For circuits containing dependent sources or/and independent sources

When a circuit contains dependent sources in addition to or in absence of the independent source. Then, Thevenin’s resistance (R_TH) can be determined by using any of these two following methods.

First Method: Short-Circuit Method

Step I – Remove the load resistance.

Step II – Find the voltage V_oc across the open-circuited load terminals by using any conventional network solution method.

Step III – Now, short-circuit the load terminals and determine the short-circuit current I_sc flowing through the shorted path.

Step IV – Then, the internal resistance or Thevenin’s resistance R_TH of the network will be,

`\R_(TH)=V_(oc)/I_(sc)`

Second Method: Test Voltage Method

Step I – Remove the load resistance.

Step II – Deactivate all the independent current and voltage sources.

Step III – Apply a DC test voltage V_t at the open-circuited load terminals.

Step IV – Due to the applied voltage V_t, a direct current I_t will flow in the circuit from the load terminals.

Step V – Then, the internal resistance or Thevenin’s resistance R_TH of the circuit will be,

`\R_(TH)=V_t/I_t`

Hence, using any of these above methods, we can find the internal resistance or Thevenin’s resistance of a given electric circuit.