Saturday, September 1, 2012

SOLVED PROBLEMS ON THEVENIN'S THEOREM (1)


SOLVED PROBLEMS


Q1) Determine the thevenin’s equivalent  circuit between the terminals A&B For the circuit shown in figure 11.1 .



Answer:

First we are about to find the thevenin’s resistance. To find the thevenin’s resistance we remove the resistance RL and open circuit the AB terminals. Then we remove the voltage source and short circuit it. See figure 11.2



We can easily find the thevenin’s resistance now.

Rth = (5//10 + 3)


Now we have to find the thevenin’’s voltage. For this we remove the load resistance RL . See figure 11.3

Note that there is no current flow through 3ohms resistance as it is open ended from point A. Hence in nodal equation we don’t have to add the current through this resistance.
Applying nodal equation method to point c,


(V-30)/5  + (V-0)/10  = 0

V = 20V

From figure 11.3 you can see that,

VA = VC
VA = VTH

Therefore V = VTH
VTH = 20V




Q2) Find the equivalent e.m.f of the network when viewed from terminals A&B and the equivalent resistance of the network when looked from terminals A&B and the current through load resistance RL . Refer figure 11.4




Answer:

Current in the network after load resistance has been removed (figure 11.5)


I = 24/(12+3+1)

I = 1.5A.


Applying Ohm’s law on 12  Ohm’s resistance,

Voltage across A and B = VTH = 12 Ohms x 1.5A


Now we are about to find the RTH


It is very easy. Just remove and short circuit the voltage source and find the equivalent resistance as seen from A&B terminals.

NOTE: YOU SHOULD LEAVE THE INTERNAL RESISTANCE OF THE VOLTAGE SOURCE THOUGH YOU REMOVE IT. SEE FIGURE 11.4.(a)



Rth  = (3+1)//12 = 3 Ohms

Hence we have find the thevenins equivalent circuit. So we can easily find the current through load resistance. See figure 11.5.(a)



















ILOAD = 18 / (3+15)

ILOAD = 1A

Q3) determine the thevenin’s equivalent circuit between the terminals A&B. you may refer figure 
11.6



Answer:


This network contains a current source. So it will be important to you to understand how to deal with  a current source in thevenin’s theorem.


Figure 11.7 shows the circuit to find RTH. Note that two terminals between the current source has been open circuited while the voltage source do the opposite.


RTH =  5 + { [ (10//10 ) + 2 ] // 3 }
RTH = 7.1 Ω


From figure 11.8


Voltage at point C = Vc = Vth  (as there is no current through 5Ω resistor)

We have grounded the point B to make our calculation easier.


Nodal equation to point C

(VC – 0)/3 + (VC-VD)/ 2 = 0

 5VC – 3VD = 0 -------------------------------------------(1)


Nodal equation to point D


(VD - VC)/2 + VD/10 + (VD -5)/10 – 1 = 0

 7VD – 5VC = 15 ---------------------------------------(2)

By solving 1&2

Vc  = 2.25V

VC = VTH

VTH  = 2.25V



I’ll add more examples in my next post.



PLEASE LEAVE YOUR PROBLEM AS A COMMENT. OR MAIL TO: pabindu@gmail.com


Pabindu lakshitha
B.Sc (Engineering Undergraduate)















49 comments:

  1. What happens if there is a resistance in the path where current source is located?

    ReplyDelete
    Replies
    1. in a current source, internal resistance is very high (infinite). so though we connect a resistance series with current source, it won't do a considerable change to the internal resistance of the current source.therefore we don't get that resistance in to our account.
      following link will direct you to the post about current sources.

      http://eefundamentals.blogspot.com/2012/08/direct-current-5-voltage-current-sources.html

      thank you.

      Delete
    2. In a current source the internal resistance is parallel to the current source not in series.
      The parallel resistance ideally must be infinite.
      So if we connect a resistor there will be a voltage drop of I x R

      Delete
  2. how about if the resistance is varied

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
  3. (V-30)/5 + (V-0)/10 = 0

    V = 20V

    in Q1, V-30 and V-0. Would you like explain to me about this? I am not understand yet . Tq

    ReplyDelete
  4. in the place of RL if there is a voltage is that Voc?

    ReplyDelete
  5. Replies
    1. as your wish there is no important what you are give name resistance

      Delete
    2. as your wish there is no important what you are give name resistance in the circuit importance is the which resistor are in series or parallal ok

      Delete
  6. if resistance varies through in path of current how then we compare there.

    ReplyDelete
  7. Quite helpful....bt plz post some more solved problems based on circuit having current depending voltage source

    ReplyDelete
  8. Is the Vth value in 3rd question correct?? because i'm getting 0.75

    ReplyDelete
    Replies
    1. I am getting same Vth=2.25volt

      Delete
    2. for do that problem just do like this
      10/10+5*32
      then we will get vth value

      Delete
    3. wrong but the vth value is 11.25

      Delete
  9. in Q 2) HOW thevinins voltage is calculated??????

    ReplyDelete
  10. how we solve when 10ohm and 3 ohm resistor are ground directliy plz reply

    ReplyDelete
  11. I didn't get how you wrote the equation at nodal D in 3 problem while finding out Voc

    ReplyDelete
  12. If a battery is connect near to point B (in series)??? What will happen???
    Is Vth value changes????

    ReplyDelete
  13. i, understand topic easily but, i have
    A small doubt, in finding the vth only
    A method of nodal is done or not
    And sent some more problems with examples

    ReplyDelete
  14. i, understand topic easily but, i have
    A small doubt, in finding the vth only
    A method of nodal is done or not
    And sent some more problems with examples

    ReplyDelete
  15. in your next post please solve using kirchoffs law

    ReplyDelete
  16. 0-vc/3 + Vc-Vd/2 = 0

    Is the correct equation no. 1 !

    ReplyDelete
  17. This comment has been removed by the author.

    ReplyDelete
  18. if there is no 10 ohm resistor in figure 11.6 then what are the two equation for solving Vth? can you please help me?

    ReplyDelete
    Replies
    1. Wish you are mentioning the 10 ohm resistor at point D in parallel with the current source.
      (VC – 0)/3 + (VC-5)/ 12 = 0

      Solve this an find Vc.
      Then
      (VD - VC)/2 + (VD -5)/10 – 1 = 0
      Find Vd.
      You must re calculate Rth without 10 Ohms resistor.

      Delete
  19. what if in question 3 I add a voltage source in series with 5 ohm resistor which was neglected in calculating the Vth . Will the voltage source be neglected too and Vc=Va hold true?

    ReplyDelete
  20. Using Thevenin’s theorem, what is the load
    current in Fig. 1-9a for the following values of RL: 2 kV, 6 kV, and 18 kV?
    If you really want to appreciate the power of Thevenin’s theorem, try
    calculating the foregoing currents using the original circuit of Fig. 1-9a and any
    other method.


    Rth=6kohm
    24v

    ReplyDelete
  21. Replies
    1. Thank you for selecting the best forum to say it

      Delete
  22. Why ideal current is subtracted in Q3?

    ReplyDelete
  23. Why ideal current is subtracted in Q3?

    ReplyDelete
  24. This has really been helpful. Please, what if the circuit only has a current source

    ReplyDelete
  25. Sir please solve the last sum in mesh analysis also

    ReplyDelete
  26. Sir please solve the last sum in mesh analysis also

    ReplyDelete
  27. This comment has been removed by the author.

    ReplyDelete
  28. (V-30)/5 + (V-0)/10 = 0

    V = 20V [why is it (+), so does that mean both current enters the node? and (v/10) is a current that's from the ground??]

    ReplyDelete
    Replies
    1. This comment has been removed by the author.

      Delete
    2. Hellow Hans Lim,
      It seems you must study nodal equation method. Please follow below link which will lead you to my post on nodal equation method.
      Take 30 mins and study this post. It will solve all your problems.
      https://eefundamentals.blogspot.com/2012/08/network-analysis-3.html

      Thank you.
      Pabindu Gamage.
      B.Sc Eng (Hons)

      Delete
  29. also from what i learned its higher potential to lower potential, (30-v)/5 :/ cauuse there would probably be a voltage drop. idk i wnna clear things up

    ReplyDelete
    Replies
    1. Hellow Hans Lim,
      It seems you must study nodal equation method. Please follow below link which will lead you to my post on nodal equation method.
      Take 30 mins and study this post. It will solve all your problems.
      https://eefundamentals.blogspot.com/2012/08/network-analysis-3.html

      Thank you.
      Pabindu Gamage.
      B.Sc Eng (Hons)

      Delete
  30. send more problems with dependent sources

    ReplyDelete
  31. how can we actually know where to use nodal analysis method?
    we can also use the Kirchoff's laws to find Vth Rth right. So basically where exactly we can use nodal analysis method?

    ReplyDelete
  32. Why you minus by on the Vd nodal analysis

    ReplyDelete
  33. Thanks for good examples
    These helped me to understand better

    ReplyDelete

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