What is transient in AC circuit? and why it is Necessary??

 ✱WHAT IS TRANSIENT?

➝"Transient is occurs due to the sudden change in the supply voltage or change in  energy stored by memory element (Inductor or capacitor) is called as a transient". 

➝The time taken by memory element to comes from one steady state value to another steady state value is referred as a Transient time or response of an ac Circuit.

• Electrical Network or Circuit is mainly consisting of three elements, which are ;

1. RESISTANCE (R)
2. INDUCTOR (L)
3. CAPACITOR (C)

• Out of this three elements Inductor (L) and Capacitor (C) are memory elements because it stored energy proportional to the 1/2 L×I^2 and 1/2 C×V^2 respectively, but Resistor (R) is memory less element because it doesn't stored any energy in it.
• Now we are studying standard discharging and normal discharging equation.

❋STANDARD DISCHARGING EQUATION:-

                              y0 (t) = y0 e^-t/τ .........(1)

Where; τ= Time constant

Assuming various value of time constant 0, τ, 2τ, 3τ, .........∞

     y (t=0) = y0 × e^-0  = y0

     

        y (t=τ)  = y0 × e^-1  =0.367 y0

        

        y (t=2τ)  = y0 × e^-2  =0.135 y0

         

          y (t=∞)  = y0 × e^-∞  =0

Fig (a) STANDARD DISCHARGING CURVE.

➝As shown in the above figure behaviour of standard discharging.

❋NORMAL DISCHARGING EQUATION:-

                 y(t) = K + y0 × e^-t/τ ...........(2)

   Assuming various value of time constant 0, τ, 2τ, 3τ, .........∞           

       y(t=0) = K + y0 × e^-0  = K +y0 

      y(t=τ) = K + y0 × e^-1  = K +0.368y0 

      y(t=∞) = K + y0 × e^-∞  = K

Fig (b) NORMAL DISCHARGING CURVE.

• Please remember in Network Theory "t = 5τ" is called as a SETTLING TIME.
• "SETTLING TIME IS DEFINED AS A TIME AT WHICH RESPONSE OF THE NETWORK IS COMES TO STEADY STATE REGION IS CALLED AS A SETTLING TIME OF NETWORK".

• From the above discussion we conclude that Ideally the memory element (Inductor or capacitor) is DISCHARGED TO ZERO but Practically it doesn't discharge to Zero (few amount of energy is stored in it).

    ....................Thank you 🙂..........

        

What is Two port and One port Networks???

• ONE PORT NETWORK:-

➝ A Network is considered as a rectangular box with Two input terminal are called as a ONE PORT OR SINGLE PORT NETWORK.

Fig(a) ONE PORT NETWORK

• TWO PORT NETWORK:-

➝A Network is considered as a rectangular box with Two input terminal and Two output terminal are called as a Two port Networks or Four terminal Network.

Fig(b) TWO PORT NETWORK

• 
  DIFFERENT PARAMETERS OF TWO PORT NETWORK:-

1. IMPEDANCE OR OPEN CIRCUIT "Z" PARAMETER.
2. "Y" - PARAMETER OR SHORT CIRCUIT PARAMETERS.
3. "H" - PARAMETERS OR HYBRID PARAMETERS.
4. TRANSMISSION PARAMETERS OR ABCD PARAMETERS.

❋ OPEN CIRCUIT "Z" PARAMETER:-

Fig(c) Z PARAMETER

⇨Consider the above Network in this two port network each input voltage V1 and output voltage V2 is expressed in terms of input current I1 and Output Current I2 respectively.

⇨According to ohm's law........

                           V = R×I 

   But here,.  R = Z so,

                          [V] = [Z]×[I] ................(1)

⇨In matrix form..........

                                                     ..................(2)

⇨From the figure of two port network we can write down the equation of V1&V2 which is exactly Same as KVL equation..........

                   V1 = Z11×I1 + Z12×I2 ..............(3)

                   V2 = Z21×I1 + Z22×I2 ..............(4)

➝ASSUMING OUTPUT PORT IS OPEN CIRCUITED (I2=0):-

    Put I2= 0 in Equation Number (3)&(4)......

                    V1= Z11×I1 

                ∴ Z11 = V1/I1|I2=0 ......................(5)

  And.         V2 = Z21×I1 

                ∴ Z21 = V2/I1|I2=0 ......................(6)

➝ASSUMING INPUT PORT IS OPEN CIRCUITED (I1=0) :-

   Now put I2=0 in Equation Number (3)&(4)......

                     V1 = Z12×I2 

                  ∴ Z12 = V1/I2|I1=0 ....................(7)

                    V2 = Z22×I2 

                     V2 = Z22×I2

                  ∴ Z22 = V2/I2|I1=0 ................,...(8)

Where ;

• Z11&Z22 = DRIVING IMPEDANCE OF INPUT AND OUTPUT RESPECTIVELY.
• Z12&Z21 = TRANSFER IMPEDANCE OF INPUT AND OUTPUT RESPECTIVELY. 

✱EQUIVALENT MODEL OF"Z" PARAMETER:-

Fig(d) EQUIVALENT MODEL OF Z PARAMETER

   .....................Thank you 🙂👍...................

                    

                   

Why SILICON material is mostly preferred for manufacturing POWER ELECTRONICS COMPONENTS??

• First we will see what is power electronics?

➝ " Power Electronics is the branch of electronics that deals with controls and conversion of large power"

➝In power electronics special power electronics components like IGBT (INSULATED GATE BIPOLAR JUNCTION TRANSISTOR), SCR ( SILICON CONTROLLED RECTIFIER), GTO (GATE TURN OFF THYRISTOR), MOSFET( METAL OXIDE SEMICONDUCTOR FIELD EFFECT TRANSISTOR), ETC. Are used for various purposes like VARIABLE FREQUENCY DRIVE (VFD), AUTOMATIC VOLTAGE CONTROLLED (AVC), AUTOMATIC SPEED CONTROL OF INDUCTION MACHINES, etc.

• ADVANTAGES OF POWER ELECTRONICS:-

⇨It has high efficiency.

⇨Reliable and flexible operations.

⇨It is possible to make fully automatic system.

⇨Less maintenance is required.

• DISADVANTAGES OF POWER ELECTRONICS:-

⇨Power Electronics devices produced harmonics in the system and due to harmonics disturbance are produced in the system.

⇨Power Electronics devices are costly.

❇️WHY SILICON MATERIAL IS MOSTLY PREFERRED FOR MAKING POWER ELECTRONICS COMPONENTS?

• SOME IMPORTANT POINTS:-

1. Band :- Band is defined as the collection of energy.
2. Conduction Band:-  It is the band which is partially filled with electrons or empty.
3. Valance Band :- It is the band which is fully filled with free electrons at 0° absolute temperature.
4. Energy Gap : It shows amount of energy which is required to moves free electrons from valance Band to conduction band.
5. Conductivity :- Conductivity is the ability of the material to pass charge or free electrons through it.

• Energy gap diagram of GERMANIUM and SILICON material;

Fig(a) ENERGY GAP OF GERMANIUM AND SILICON.

                            Eg = 1/ σ ...................(1)

 Where :- 

                  Eg = Energy gap 

                   σ  =  Conductivity of material

 

       From figure ;

             σGe = 1/.73

                      = 1.369 ................(2)

               σSi =  1/ 1.1

                      = .909 .................(3)

So we know that 

                             σGe > σSi

From this calculation we understand that conductivity of GERMANIUM IS GREATER THAN the conductivity of SILICON.

✲BUT DUE TO THE FOLLOWING REASONS SILICON MATERIAL IS MOSTLY PREFERRED:- 

Fig (b) COMPARISON BETWEEN GERMANIUM AND SILICON

• After studying this above TABLE we conclude that SILICON MATERIAL IS MOSTLY PREFERRED FOR MAKING POWER ELECTRONICS COMPONENTS.

       ...............Thank you 🙂👍...............

What is RESONANCE in series RLC circuit????

• RESONANCE:-

➝ " It is the phenomenon at which the effect of Inductive reactance (XL) and Capacitive reactance (XC) are compensated to each other in RLC circuit is called as a RESONANCE".

➝At the time of resonance circuit is behaves as a pure resistive circuits and at the time of resonance power factor of the circuit is UNITY.

❋RESONANCE IN SERIES RLC CIRCUIT:-

Fig(a) SERIES RLC CIRCUIT

⇨The Impedance Z of series RLC circuit is given as;

                 Z = R + jwL + j 1/WC

            ∴.  Z = R + wL - j/wc ................(1)

Magnitude

 |Z| = √R^2 + j( wL - 1/WC)^2 ...........(2)

➝ Current in RLC resonance circuit is;

                  I = V/Z amp. ..........(3)

          I = V/ √R^2 + j(wL - 1/WC)^2 ㄥ tan-1 (wL - 1/WC)/R   ...................(4)

• AT THE TIME OF RESONANCE XL = XC ;

                 XL = XC

              W0L = 1/ W0C 

               W0^2 = 1/ LC

          ∴ W0  = 1/ √LC rad/ Sec ...........(5)

• Frequency at the time of resonance ;

                     

                   W0 = 1/ √LC rad/ sec ....... ..(6)

                    

                   F0 = 1/ 2π√LC Hertz (Hz) .......(7)

❋ PROPERTY OF SERIES RLC RESONANCE CIRCUIT:-

⇾At the time of resonance the applied voltage is in phase with resultant current, it means the power factor is unity (COSΦ = 0).

⇾At the time of resonance the effects of XL &XC are compensated to each other, therefore the behaviour of the network is purely RESISTIVE.

⇾At the time of resonance the Current I = V/R amp. And it's value is maximum because total impedance of the circuit at the time of resonance is only "R" so I is maximum according to ohms law.

⇾At the time of resonance the Impedance Z is minimum.

           .................... Thank you 🙂................

What are the property of INCIDENCE matrix? Why we used it in Network analysis?

• INCIDENCE MATRIX:-

➝ "Incidence matrix is the mathematical representation of node current and voltage in various branches of the network".

➝Incidence matrix is used to describe the Nature of Incoming and Outgoing branches across any nodes in the Network.

➝Order of Incidence matrix is;

                 [A]n×B.    

           Where; n = Numbers of node

                          B = Number of branches 

• HOW TO MAKE INCIDENCE MATRIX OF GRAPH:-

Fig(a) GRAPH OF NETWORK

• Before making Incidence matrix of any graph following points are keep in mind.

⇨ +1 = If Direction of current is Away from node.
⇨ -1  = If Direction of current is Towards the node.

⇨ 0   =  If note Incidence 

• Now select any one node and check direction of current in all branches of the network corresponding to this particular node.
• Suppose we consider Node "A" please observed in fig (a) direction of current in branch 1 is towards the node so it is -1, and direction of current in branch 2 & 6 is away from the node so it is +1 and finally branch 3,4&5 are not Incidence so it is 0.
• All this steps are perform by taking one by one nodes.
• Finally we get Incidence matrix as shown in below figure.

Fig(b) INCIDENCE MATRIX OF GIVEN GRAPH 

✱PROPERTY OF INCIDENCE MATRIX:-

➝ Summation of all the columns of Incidence matrix is equal to ZERO.

➝ If the network ha Number of nodes is equal to numbers of branches (n = B) then the resultant Incidence matrix is a SQUARE MATRIX.

➝ The determinants of square matrix is always ZERO.

" INCIDENCE MATRIX IS USED TO FIND THE POSSIBLE TREES OF ANY NETWORKS WITHOUT DROWNING IT".

        .................THANK YOU 🙂.................

Concept of NETWORK TOPOLOGY.

• First we will discussed some important definition and then we will learn how to make GRAPH from any given NETWORKS.

❇️ IMPORTANT DEFINITIONS RELATED TO NETWORK TOPOLOGY;

1. GRAPH :- When all elements in the Network like Inductor, capacitor, Resistance etc. Are replaced by simple single line with small circle at both the ends then this type of configuration is called as a GRAPH.
2. NODE OR VERTICES :- Node is defined as the intersection of two or more branches at one common point is called as a NODE OR VERTICES.
3. BRANCH :- Branch of network is defined as a line which represents one Network element or combination of elements connected between two common point.
4. DEGREE OF NODE :- Degree of node is defined as the number of incoming branches across any node.
5. COMPLETE GRAPH :- A graph in which only one line segment is connected between any node pair is referred as a COMPLETE GRAPH.
6. NON CONNECTED GRAPH OR UN CONNECTED GRAPH :- A graph in which any node is isolated ( means no any branch is connected between this node) is known as a Non connected or un connected graph.
7. ORIENTED GRAPH :- A graph in which direction of current is indicated in all the branches then it's called as a ORIENTED GRAPH.
8. NON ORIENTED GRAPH :- A graph in which the direction of current is not indicated then it's know as a NON ORIENTED GRAPH.

❋Now we take one example and learn how to draw GRAPH of any random given NETWORKS.

Fig(a) ANY RANDOM ELECTRICAL NETWORK

➡️ STEPS TO MAKE GRAPH FROM ANY NETWORK :-

⇾Fisrt identify numbers of nodes in the given network and mark it as 1,2,3.... Or a,b,c.... Or p,q,r......etc.

⇾After identify nodes represent each node as circle in paper (number of node = number of circle).

⇾Now replaced all the network element like Inductor, capacitor, resistance etc with simple one line.

⇾Replaced all independent voltage sources with short circuit and all independent current sources are open circuit.

⇾Finally connect all this line segment with their respective nodes.

⇾Graph of network is ready but it is non oriented graph if we like to make oriented graph then assign direction of current in all the branches with respect to given source in the Network.

Fig(b) GRAPH OF THE GIVEN NETWORK.

• For any complete graph if we know number of nodes then we easily calculates number of branches of network.

           

  For any complete graph number of branches ;.        

                      B = n×(n - 1)/ 2............(1)

Where ; n = Numbers of nodes

        ................... Thank you 🙂....................

Why transformer doesn't work on DC supply???

• Before understanding this concept first we need to know working principle of transformer.

Fig (a) Working principle of transformer

• Working principle of transformer:-

➝ Transformer is works on the principle of MUTUAL INDUCTION.

➝ According to principle of MUTUAL INDUCTION, if time varying current (AC CURRENT) is given to the primary winding of transformer then it produces the time varying flux and due to this time varying flux EMF is induced in the primary winding, we already discussed in the previous article some amount of this primary winding flux is linked with secondary winding also, so EMF is induced in seconady Winding due to rate of change of current in the primary winding.

• Consider the equation of induced voltage in inductor or Coil;

Induced voltage V = -N di/dt ................(1)

                Where; - (minus) sign is due to LENZ LAW

                                 di/dt = Rate of change of current

❇️ CASE NUMBER :-1 INPUT IS AC

Fig (b) Input Sine wave

⇨According to Faraday's law we know that voltage is induced in the coil if and only there is relative motion between Conductor and Magnetic field.

⇨Suppose if we connect Sinusoidal input supply with primary of transformer then it produces time varying flux so EMF is induced in the primary winding and we know that supply is Sinusoidal EMF is also induced in the secondary winding due to rate of change of flux in the primary.

⇨So if we connect AC SUPPLY to the primary winding of transformer then transformer is satisfactory work with ac supply.

❇️CASE NUMBER :-2 INPUT IS DC

Fig (c) Input DC supply

⇨Suppose if we connect DC supply with primary winding of transformer, then it produces CONSTANT FLUX, Because DC is constant source it's value remain constant.

⇨Due to DC rate of change of flux will be Zero, so induced voltage in the primary winding will be ZERO.

                V = -N di/dt 

HERE di/dt = zero so V=0 means short circuit

• PLEASE OBSERVED VOLTAGE ZERO MEANS SHORT CIRCUIT, SO RESULT IS THAT THERE IS AN EXCESSIVE LARGE CURRENT IS FLOW THROUGH THE PRIMARY OF TRANSFORMER, DUE TO THIS LARGE CURRENT PRIMARY OF TRANSFORMER IS DAMAGED AFTER FEW TIME.
• So, from above discussion we conclude that TRANSFORMER DOESN'T WORK ON DC SUPPLY.

            ....................... Thank you 🙂.....................

Why DIODE is a non linear device???

• Ideal Diode:

➝ We know that an Ideal Diode is work same as an Ideal switch as discussed earlier.

➝Ideal Diode does not consume or Absorb any power from the source it means it has zero internal resistance and power loss.

Fig(a) Symbol of an Ideal Diode

• DEFINITION:-

➝"An ideal diode is one type of electronic switch (Ideal Switch), it allows to pass the current in only one direction ( ANODE TO CATHODE)".

Fig(a) working of an Ideal Diode

✱ DURING POSITIVE HALF CYCLE OF AC SUPPLY:-

⇨During the positive half cycle of ac supply P (anode) terminal of diode is connected to the +Vin and N (cathode) terminal of diode is connected to the-Vin of ac supply, so diode is in forward bias and start conducting.

⇨During forward biasing of diode current I is start to increasing and flows through the load.

✱DURING NEGATIVE HALF CYCLE OF AC SUPPLY:-

⇨During the Negative half cycle of ac supply P (anode) terminal of diode is connected to the-Vin and N (cathode) terminal of diode is connected to the +Vin of ac supply, so diode is in reverse biase.

⇨We know that diode doesn't allow to flow current in reverse biase, so that whole Negative half cycle of ac supply is BLOCKED across the Diode.

Fig (c) waveform of given circuit

• From the waveform we clearly understand that during positive half cycle of ac supply output is changed with respect to input but during the negative half cycle of ac supply, output remain ZERO during whole Negative half cycle.

➝So, from the above discussion and waveform we conclude that AN DIODE IT SELF SOWS NON LINEARITY, it means output does not follow input.

             ................Thank you 🙂................

How PRACTICAL DIODE works???

• To understand the working of practical diode, first we need to know the difference between an IDEAL DIODE and PRACTICAL DIODE. 

• Difference between an Ideal Diode and Practical Diode.

1. An Ideal Diode is behaves same as an Ideal switch. There is zero voltage drop across it.
2. But Practical Diode is replaced by its cut-in Voltage.
3. An Ideal Diode doesn't consume any power from the source during its operations.
4. Practical diode consume some amount of power from the source.
5. Ideal diode is replaced by short circuit when it is forward bias whereas an practical diode is replaced by an cut-in Voltage when it is forward bias. 

❋PRACTICAL DIODE:-

⇨Practical diode is conducted if an only the supply voltage is greater than its cut-in Voltage.

"Cut-in Voltage is the minimum potential required for satisfactory conduction of diode is known as a cut-in Voltage".

Fig.(a) Symbol of Practical Diode

• Cut-in Voltage is denoted by =Vλ
• If diode is Made up if GERMANIUM = Vλ = 0.3 Volts
• If diode is Made up of SILICON = Vλ = 0.7 Volts.

Fig(b) Use of Practical Diode in Circuit

Fig(c) Out put waveform

❇️ DURING POSITIVE HALF CYCLE OF AC SUPPLY:-

• At t=0 ; the value of Vin = 0 volts so diode D doesn't conduct this state of diode is called as a FORWARD BLOCKING MODE, when Vin> 0.7 Volt (for silicon) at that time diode is start to conducting, this state of diode is called as a forward conduction mode. During forward conduction mode diode is replaced by short circuit and current start to flow from P to N terminal of diode, Load and Vin and output voltage is obtained across the load RL.

❇️ DURING NEGATIVE HALF CYCLE OF AC SUPPLY:-

• During Negative half cycle of ac supply P terminal of diode is connected to the -Vin and N terminal of diode is connected to the +Vin of ac supply so diode is reverse biase and out put voltage across the load is zero during whole Negative half cycle as shown in waveform.

☺V-I characteristics of an practical diode:-

Fig(d) I-V characteristics of an practical diode

Where;  Vλ = Cut-in Voltage

                I0. = Reverse saturation current

• Reverse saturation current:-

" It is current of diode which is flows due to the minority carriers".

            ...................Thank you 🙂.................

How Ideal Diode is work??

• IDEAL DIODE:-

Fig(a) Symbol of Diode

⇒An ideal diode is behaves same as an Ideal switch.

• Behaviour of an Ideal Switch:

Concept of MUTUAL INDUCTUNCE and MAGNETIC COUPLING

• Definition of Mutual Induced emf:-

➝ " It is defined as the emf is induced in the coil due to the rate of change of flux is occurs in the nearest coil which is linked with it".

• EXPLANATION:-

Fig.(a) MUTUAL INDUCED VOLTAGE

Whre; 

             N1 = Numbers of turns of Coil A

             N2 = Numbers of turns of Coil B

             R.   = Variable Resistor

              G.  = Galvanometer

         Φ12. = Flux of coil A is linked with Coil B

         Φ21 = Flux of Coil B is linked with Coil A

➝ When supply voltage V is connected across Coil A then current I1 is flows through the coil A due to this current flux Φ1 is produced in the coil A, the direction of this flux Φ1 is found by RIGHT HAND CURL RULE as discussed in previous article.

➝ According to RIGHT HAND CURL RULE if the direction of current is in the direction of Curl then right hand thumb will represent the direction of magnetic field as shown in below figure.

➝ Some portion of this flux Φ1 is called as Φ12 is linked with Nearest Coil B, Now if we change the current I1 by changing the value of Variable Resistor R then flux Φ12 which is linked with Coil B is also change and due to this rate of change of Flux in Coil A, EMF is induced in nearest coil B and vice varsa. The direction of induced EMF in Coil B is found by RIGHT HAND CURL RULE.

• What is MUTUAL INDUCTUNCE?

⇨Mutual inductance is the property of the coil which Oppose the change of current in nearest coil.

                   M12 = N2 × Φ12/ I1 ...............(1)

                 M21 = N1 × Φ21 / I2 .............(2)

Now,. Suppose M12 = M21 = M

• Coefficient of Coupling (K):-

➝"Coefficient of Coupling K is describe the capability of flux linkages" OR it is defined as the fraction of the total flux that links with the Coil.

                 i.e.   K = Φ12/ Φ1 = Φ21/ Φ2 .......(3)

• Multiply equation number (1)&(2) with equation number (3) ..............

  M^2 = N1 × N2 × Φ12×Φ21/ I1×I2  × Φ1Φ2/ Φ1Φ2 .............(4)

• Rearrange term in above equation.......

    = N1Φ1/ I1 × N2Φ2/I2 × Φ12/ Φ1 × Φ21/Φ2 

     =  L1 × L2 × K × K 

• NOTE:- 

           L1 = N1Φ1/ I1

           L2 = N2Φ2/I2

             K = Φ12/ Φ1

             K = Φ21/Φ2

        ∴ M^2 = L1 × L2 × K^2

              M = K × √L1×L2 ...........(5)

        ∴ K = M/ √L1×L2 .............(6)

        ............Thank you 🙂.............

Concept of SELF INDUCTUNCE.

What is SELF INDUCTUNCE?

⇨ If an time varying current is passing through the Coil or Winding, it produces the time varying flux this flux is linked with it self and voltage is induced in the coil or Winding is called as a SELF INDUCED VOLTAGE.

                   V = L di/dt ................(1)

Fig.(a) SELF INDUCED VOLTAGE

• Why inductor oppose the rate of change of current?

➝we know that due to time varying current self induced voltage is induced in coil, this is shown by V. Magnetic field within it is try to maintain its value constant. But if at any intant supply current is disturb then this self induced voltage create a current which Oppose the rate of change of supply current (according to Lenz's law).

Now, the inductor L is expressed as,

                          L = NΦ/ I ................(2)

Where; N = Number of turns of Coil

               Φ = Flux linkage with coil

               I = Current passing through the

Coil

 

• Substitute equation number (2) in (1)......

                            I = NΦ/L ..................(3)

Now putting the value of I in equation number (1) we get.........

               V = L × d (NΦ/L) / dt

             ∴  V = L × 1/L × N  dΦ/dt

             ∴ V = N × dΦ/dt ..............(4)

• Comparing equation number (1)& (4)........

           L × di/dt = N × dΦ/dt

As seen "dt" is cancelled out ......

Finally we get value of INDUCTUNCE "L" is......

                       L = N × dΦ/ di 

        ............Thank you 🙂............

Concept of SUPER MESH.

"If an IDEAL CURRENT SOURCE (Dependent OR Independent) is common between two meshes then it is referred as a SUPER MESH by avoiding Ideal current source".

Q. Why Concept of SUPER MESH is developed?

➝ The concept of SUPER MESH is developed because it reduce the number of meshes in the network.

➝ In previous article ( If we doesn't have any idea about SUPER NODE then what we do???) We learn that if any ideal voltage source is present in the Network then we need to assume current of an Ideal Voltage Source similarly if any ideal current source is present in the network then we need to assume voltage of an Ideal current source. 

➝so from above discussion we conclude that concept of SUPER MESH is developed to avoid assumption of Voltage of an Ideal current source.

• Important points regarding SUPER MESH:-

1. A SUPER MESH has no current of it's own.
2. A current source in SUPER MESH provide equation which is necessary for solving of Mesh Current.

☺ Consider the Network as shown in below figure, Find the Value of current "I" ______in Amp.

Fig.(a) Find the value of I

• SOLUTION:-

If any ideal current source is COMMON between two meshes then super mesh is form by avoiding Ideal current source present in the network.

Fig(b) Represent Super Mesh 

In this figure ;

                I1 =  current flow through Mesh(loop) 1

                I2 =  Current flow through Mesh (loop) 2

Blue Dotted Line Represent SUPER MESH please observed in Figure.

• KVL OF SUPER MESH:-

      -10 + I1×1 + I2×3 + 5 = 0 

   ∴ I1 + 3I2 = 5 .................(1)

• KCL OF SUPER MESH:-

          I2 - I1 = 2 .................(2)

NOTE; in figure I2 is in the Direction of 2 AMP current source so it's direction is taken as POSITIVE and I1 Oppose the 2AMP current source so its direction is taken as a NEGATIVE please seen in figure (b).

• Adding equation number (1)&(2) we get.....

           I1 + 3I2 =5

           -I1 + I2 = 2                       

         ______________

                    4I2 = 7 

So,.           I2 = 7/4 AMP.

AS SHOWN IN FIGURE ;

                          I2 = I 

                 

                      

                  I = 7/4 AMP.   

                 

Can we do supernode questions by using only nodal analysis?

• Answer is YES.

➝ If we don't know about super node then we used simple node equation to solve any network contain super node.

• Before understanding this concept first we need to understand basics of Practical voltage source and Ideal Voltage Source:-

✱Practical Voltage Source:

➝ Voltage source in series with Internal Impedance (Zin) is referred as practical voltage Source.

➝Value of this internal Impedance is as low as possible,  Because if the value of Zin is high then Voltage drop across Zin is also high so voltage at load point or Terminal is Low. So it is required to choose the value of Zin is as low as possible.

Fig (a) Practical voltage source

✱ Ideal Voltage Source:

➝ Internal Impedance Zin of any practical voltage source is tends to ZERO is referred as Ideal Voltage Source.

➝It is important to know that "CURRENT OF ANY IDEAL VOLTAGE SOURCE IS NOT ZERO" , Because resistance of any ideal voltage source is tends to Zero not exactly Zero so that CURRENT  through the source is tends to Infinite, It means  Ideal Voltage Source is capable to deliver unlimited power.

Fib(b) Ideal Voltage Source

➡️ Consider the Network as shown in below figure, Find the Value of Vp_____& Vq_______in Volts Without using concept of SUPER NODE.

In this above network 5V source is Ideal Voltage Source so we assume current of an Ideal voltage source is "I". Direction of this current is assuming Negative terminal to Positive Terminal ( because current is always flow from Higher potential to lower potential).

• Applying Simple Node equation at Node Vp..............

       Vp-10/1 + Vp/2 - I =0 .............(1)

• Applying Simple Node equation at Node Vq.....,.......

       Vq/3 + Vq-10/4 + I =0 ..............(2)

➝Adding equation number (1)&(2).............

At that time "I" will be canceled out Please observed in equation.........

After adding equation number (1)&(2).........

   Vp-10/1 + Vp/2 + Vq/3 + Vq-10/4 = 0 ........(3)

Please observed equation number (3) is Same as Super Node equation......

      Vp- Vq = 5 .............(4)

Now find out Vp and Vq from Equation Number (3) & (4)............

Multiply by 12 in Equation Number (3)........

12Vp - 120 + 6Vp + 4Vq + 3Vq - 30 =0

Simplified........

18Vp + 7Vq =150 .............(5)

Now multiply 7 in Equation Number (4).........

7Vp - 7Vq = 35 ............(6)

Adding equation number (5)&(6)...........

After adding we get 

        25Vp = 185

∴ Vp = 7.4 Volt

Put value of Vp in equation Number (4.).....

            5 = Vp - Vq

        ∴ Vq = 7.4 - 5

           Vq = 2.4 Volt

So without using concept of SUPER NODE we can easily solving Any questions.

          ...............Thank you 🙂...............

Concept of SUPER NODE.

• What is a NODE? 

➝When tow or more branches of any Electrical network are meeting at a common point then this common point is referred as a NODE.

• What is a SUPER NODE?

➝"If any ideal voltage source ( Dependent OR Independent) is connected between two Non reference node then this two Non reference node forms a Generalized Node is called as a SUPER NODE".

• Some Important Points:-

1. Super node does not have its own Voltage.
2. Super node required both Application of KVL ( Kirchhoff's Voltage law) and KCL (Kirchhoff's Current Law).
3. The Voltage inside the Super Node provide the equation which is necessary for calculation of Node Voltage.

 

 ➝Now we understand it by considering one example:

EXAMPLE:1

            Consider the Network as shown in below figure, Find the value of Vp _____ and Vq________volts.

Fig(a) Explanation of concept of SUPER NODE

Super node is combination of both KVL+KCL EQUATION

• KCL EQUATION OF SUPER NODE;

      

     Vp-10/1  + Vp/2 + Vq/3 + Vq-10/4 =0 ..........(1)

     Vp - Vq =5 .............,....(2)

Now find out Vp and Vq from Equation Number (1) & (2)............

Multiply by 12 in Equation Number (1)........

12Vp - 120 + 6Vp + 4Vq + 3Vq - 30 =0

Simplified........

18Vp + 7Vq =150 .............(3)

Now multiply 7 in Equation Number (2).........

7Vp - 7Vq = 35 ............(4)

Adding equation number (3)&(4)...........

After adding we get 

        25Vp = 185

∴ Vp = 7.4 Volt

Put value of Vp in equation Number (2).....

            5 = Vp - Vq

        ∴ Vq = 7.4 - 5

           Vq = 2.4 Volt

      ..................Thank you 🙂................

 

Why in LARGEST POWER STATION per phase individual transformers are used instead of one big transformer???

 ⇨I visited in ADANI THERMAL POWER STATION Mundra Gujarat. The capacity of the power station is approximately 4650MW in this power station I seen that in per phase one individual transformer are kept Instead of One Big three phase transformer.

⇨It is because for such big power station if we used one transformer then it becomes too much large approximately some MW to Few GW rating of transformer are required.

⇨If we assume to use such big transformer then it becomes too difficult to handle it and also the weights of core and winding, volume of oil in the tank, Auxiliary equipments like breather, Colling system, conservator tank, Buchholz relay etc. The Summation of weight of all this accessory are in TONNES so it is too much difficulty in transportation.

⇨Also suppose any major fault is occurs in such big transformer then first it is isolate and it's all the parts are overhauling and then faulty parts are repair after this repairing agin all parts are assemble during this entire period all the consumers are Deprived of Electricity it is big disadvantage of Use of one Big transformer.

Fig(a) Approximate Specifications of Power transformer

⇨Please observed in above table, in this table technical specifications of some MW power transformer are given from it we know that the total weight of transformer is in TONNE specially for above specifications the total weight is 233.2 tonne (1 tonne =1000 kg).  so it not easy to transport it from Manufacturers to power station site.

➝ To avoid this all above difficulty in transportation and handling of power transformer and to increases the reliability of the power system it is preferable to use PER PHASE INDIVIDUAL TRANSFORMER INSTEAD OF ONE BIG TRANSFORMER.

        ...............THANK YOU 🙂............

Zero Level Concept of HARMONIC

• What is harmonic?  

"Harmonic is defined as the unwanted signals present along with fundamental signal."

Harmonic will creates the disturbance in system and also due to presence of harmonic losses are increases.

How harmonics are produced in the system?

➝Non linear components likes Diode, Thyristor, Transistor, Diac etc are used in the system for various purposes like AC to DC converter, Variable voltage variable frequency operations (VVVF), Automatic Power factor correction etc. This non linear components will introduce the harmonic in the system due to switching.

• Amplitude and frequency of signal along with harmonic:-

1. Amplitude "Am"(harmonic) = 1/n^2 * Am(fundamental)

Frequency "f"(harmonic) = n*f (fundamental)

Where; 

              n= integer 

Fig(a) Fundamental signal along with 3rd Harmonic

• Why 3rd harmonic component is dangerous in system compare to other harmonic?

➝ Because 3rd harmonic component is "Co-phaser phaser it means amplitude of all three phases (ia, ib, and ic) are maximum at same instant and due to Co-phaser phasor it produces the current which is peaky in nature as shown in fig (a).

☆PROOF:-

➝Assumig three phase balanced system ;

             ia+ib+ic= 0.    ................(1)

We know that in three pase balanced system all three phases are displaced in time by 120°. So that,

ia = im sin wt + im/9 sin 3wt + ..............(2)

ib = im sin wt + im/9 sin (3wt-120) + .......(3)

ic = im sinn wt + im/9 sin (3wt-240) +........(4)

NOTE:

 In equation (2),(3) and (4) we only consider odd harmonic because even harmonic is cancelled out in Fourier series.

And we only writing the equation upto 3rd harmonic because here we only prooved why 3rd harmonic is dangerous in the system

And last point is that Amplitude of current is divided by "n^2" { here, n= 3 so im is divided by 3^2 = 9).

Now only we consider 3rd harmonic component of equation (2),(3)and (4)..........

                ia                    ib                ic 

              3×0°              3×120°        3×240°

                 ↓                    ↓                   ↓

                 0°                  0°                 0°

Please shows and compare above three phases with wave form.

Fig(b) Balanced three phase system

Fig(c) Co-phaser phasor

Here; 

          3×0 = 0°

          3×120 = 360° =0°

          3×240 = 720° =0° please observed in wave form.

From the above three pase wave form we conclude that all three phases containing 3rd harmonic component are maximum and zero at same instant.

     .........................Thank you 🙂....................,