HOW TO SOLVE THEOREMS WITH BEST EXAMPLES

HOW TO SOLVE THEOREMS WITH BEST EXAMPLES:-

This blog contents some important and useful method of solving DC network circuit or Theorems and it will be helpful for those students having problems to solve direct current circuit theorems and analysis of direct current circuits laws and their application.

In this blog, I will try to provide best ideas, Solution of solving problems, Examples based on the Electrical Theorems and How to used it in solving Direct Current equations. It will be few and basic but very important ideas of solving circuits or any dc theorems. After getting all information on my blog, please try to solved it from your side and practice it at home. 

DC network is a part of physics and basic electrical engineering syllabus/paper. Basic electrical also contents ac network, induction motor, direct circuit machine transformer,etc. 

Please also be informed that it is not possible to give full tutorial in one post. So,I always keep updating my blog-post with a new topic.

(NOTE:- All topics are going to deals in my own language; it might be some grammatical mistake and some difference in their definitions but isn’t meaning that the process or solutions are also wrong.) 

 Related topics to be posted:-

A. Basic ideas about circuit

B. Ohm’s law,Current&Voltage division rule, Source conversion

C. Kirchhoff’s current law (KCL) & Kirchhoff’s voltage law(kvl)

D. Star-Delta Transformation/Conversion

E. Mesh analysis/Loop analysis/Maxwell’s loop equation

F. Nodal analysis

G. Superposition Theorem

H. Thevenin’s Theorem

I. Norton’s Theorem

J. Maximum power Transfer Theorem

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Solved Examples Problems On Star-Delta Transformation Or Conversion

Solved problem based on Norton’s Theorem

Solved Problem Based On Superposition Theorem

Example Solved Problems Based On Thevenin Theorem Circuit

Tricky Solutions For Equivalent Series-parallel Resistance Problems With Examples

Solved Problem Based On Maximum Power Transfer Theorem

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Delta To Star Transformation Or Delta To Star Conversion and Its Formulas

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Solved Examples Problems On Star-Delta Transformation Or Conversion

Solved Examples Problems On Star-Delta Transformation Or Conversion

Ques:- Find the equivalent resistance between A & B in the given network.

Solution:-

 For the given network, we can easily determine the value of equivalent resistance i.e, R_AB through  Star-Delta conversion.

We have

Above network can also be represent as below:-

Now, I am going to solved this network by using  delta to star conversion as shown in the figure given below:-

For the value of new star connected resistance are finding through direct formula of delta to star conversion,as shown below

So, R_AB / R_equivalent = R₁ + R₂ + R₃ = 4Ω + 3.88Ω + 1.77Ω = 9.65Ω Answer

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Solved Problem Based On Maximum Power Transfer Theorem

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Solved Problem Based On Maximum Power Transfer Theorem

Solved Problem Based On Maximum Power Transfer Theorem

Ques.) Find the value of R_L for the given network below that the power is maximum? And also find the Max Power through load-resistance R_L by using maximum power transfer theorem?

Solution: -

For the above network, we are going to find-out the value of unknown resistance called “R_L”. In previous post, I already show that when power is maximum through load-resistance is equals to the equivalent resistance between two ends of load-resistance after removing.

So, for finding load-resistance R_L. We have to find-out the equivalent resistance like that for this circuit:-

Now, For finding Maximum Power through load-resistance we have to find-out the value of V_o.c.

Here, V_o.c is known as voltage between open circuits.

So, steps are:-

For this circuit using Mesh-analysis. We get

Applying Kvl in loop 1^st:-

6-6I₁-8I₁+8I₂=0

-14I₁+8I₂=-6         ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ (1)

Again, Applying Kvl in loop 2^nd:-

-8I₂-5I₂-12I₂+8I₁=0

8I₁-25I₂=0             ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙ (2)

On solving,eqn (1) & eqn (2), We get

I₁ = 0.524 A

I₂ = 0.167 A

Now, From the circuit V_o.c is

V_A-5I₂- V_B = 0

V_o.c/ V_AB= 5I₂ = 5X0.167 = 0.835v

So, the maximum power through the R_L is given by:-

Solved problem based on Norton’s Theorem

Solved problem based on Norton’s Theorem

Ques.) Find-out the value of current in 4Ω resistance for the given network by using Norton’s Theorem?

Sol.) For finding value of current through 4Ω resistance, we follow same steps discussed in Previous Post.

For finding R_L: -

Here, R_L= 4Ω

For finding R_N: - For finding R_N, Just find-out equivalent b/w removed load-resistance. Like as:-

For finding I_N/I_S.C: -

 Short-circuited Pt. A and Pt.  B, we have

When we Short-circuited then all current diverted through Short-circuited path and parallel resistances will remove. Like this:-

 Applying kvl in loop 1^st:-

8-2I₁-2I₁-2I₁+2I₂ =0

-6I₁+2I₂ = -8 ··············· (1)

Applying kvl in loop 2^nd:-

-2I₂-2I₂-2I₂+2I₁ =0

2I₁-6I₂ = 0    ··············· (2)

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On solving, we get

I₁ = 1.5A & I₂ = 0.5A

Here, I₂= I_s.c/ I_N = 0.5A

Now, the Norton’s equivalent circuit is,

Example Solved Problems Based On Thevenin Theorem Circuit

Example Solved Problems Based On Thevenin Theorem Circuit

Question) Find the current in 4Ω resistance for the given network by using Thevenin's Theorem.

Solution: - For finding current through 4Ω resistance in this circuit, we follow same step as we discussed in previous post.

For R_L:-

Here, R_L = 4Ω

For R_th:-

For finding Thevenin's equivalent resistance for this network, steps are given below:-

Here, R_th/R_AB=1.5+10=11.5Ω

For V_th:-

For finding Thevenin's equivalent voltage for this network, steps are given below:-

Now,Thevenin's Equivalent Circuit is

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Solved Problem Based On Maximum Power Transfer Theorem

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Superposition Theorem And Method Of Solving Superposition Theorem

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Solved Problem Based On Superposition Theorem

Ques.) Find the current through 10 Ω resistance in the given network by using superposition theorem?

Solution:-For finding current through 10Ω resistance by using superposition theorem, we follows same step as we discussed in previous post.

Activating ‘16V’ source at a time, other will be deactivated.
 
After deactivation of ‘16A’ current source, two individual box are seem clearly in which we can easily applying mesh analysis for finding current through 10Ω resistance when ‘16V’ voltage source is active. You can  also use nodal analysis or ohm’s law with current division rule.

I am not going to discussed how to solve a circuit through mesh analysis which I already discussed. If you want to know How to solve a circuit through mesh analysis, click here.

{Hints: -    Equations are,

  -8I₁+4I₂=-16       ··············· (1)

  4I₁-18I₂=0          ··············· (2)      }

 So, after solving this circuit, we get

 I₁ =   2.25A          &          I₂ =   0.5A

Then, I_10Ω = I₂ = 0.5A

Activating ‘16A’ source at a time, other will be deactivated.

After deactivation of ‘16V’ voltage source, we can one step reduced circuit and applying current division rule. By applying current division rule, we can easily find the value of current in 10Ω resistance.

 
By current division rule,

I₁ = 4A

I₂ = 12A

So, I_10Ω = I₁ = 4A

Now, final circuit is in which all the source will be activated. Direction of current when single source is active and other is deactivated through 10Ω resistance will be shown with their value, as shown below

At last, the current through 10Ω resistance is 3.5A and greater current has their direction as shown below.

Answer: -    I_10Ω = 3.5A

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