Thevenin’s Theorem Statement: Thevenin’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources.

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Presentation transcript:

Thevenin’s Theorem Statement: Thevenin’s Theorem states that “Any two terminal linear circuit containing a large number of voltage and/or current sources and resistors can be replaced by a simple equivalent circuit containing a single voltage source and a series resistor”.

Thevenin’s Equivalent Circuit Here, V th = Voc (open-circuit voltage) R th = equivalent R (total R) in the circuit RL = load resistance of the network through which the current or across which the voltage is to be calculated Now, Current through RL = Vth / (Rth+RL)

Steps to solve circuit using Thevenin’s Theorem Calculation of V TH : 1.Remove the component of interest - normally called the load resistance(RL). 2.Mark the terminals as V TH where the load was removed from. 3.Calculate the Thevenin Voltage V TH by finding the open circuit voltage across the load terminals - remember that no current flows into an open circuit Calculation of R TH : 1.Calculate the Thevenin Resistance R TH by a. Marking the terminals as R TH where the load was removed from and setting all sources to zero (voltage sources are replaced by a short circuit and current sources by an open circuit) b.Finding the resistance between the two load terminals. 2. Draw the Thevenin equivalent circuit and return the load for analysis.

Example Find Thevenin’s equivalent circuit and the current passing through RL given RL = 1Ω

Step 1: Remove RL and mark points A and B Step 2: Find V TH ABAB i

To find R Th Short Circuit voltage source R TH Step 3: Find R TH

Thevenin’s equivalent circuit The current through RL = 1Ω is

Example Example: Find Thevenin’s equivalent circuit

Step 1:Remove RL Step2: Find V TH

Open circuit current source R TH Step 3: Find R TH

Step4: Thevenin’s equivalent circuit

Example:Find Thevenin’s equivalent circuit across RL

Step 1: Remove R L Step 2: Find V TH 0V 10V 8V 2V Here, I1=10/10=1A I2=10/5=2A I1I2 + - V TH Now, V TH - 2I - 4I = 0 or V TH - 2 ( -I1 ) – 4 (I2) = 0 Or V TH = 8 – 2 = 6V

Step 3:Find R TH R TH A B C D AB CDCD C D A B

Step 4:Thevenin’s equivalent circuit

For the circuit below, find V AB usingThevenin Theorem. We first find V TH with the 17  resistor removed. Next we find R TH by looking into terminals A-B with the sources deactivated. Example

V TH V th I I 15V

R th R TH

Thevenin’s equivalent circuit is We can easily find that,

THEVENIN’S THEOREM: Example 10.4: Working with a mix of independent and dependent sources. Find the voltage across the 100  load resistor by first finding the Thevenin circuit to the left of terminals A-B.

V TH Here, V TH = 30 Is + 6 Is Also,

Calculate the Thevenin’s equivalent circuit seen by load RL Example

V TH I

Rth

Therefore Thevenin’s equivalent circuit is 7V 3.33