Electrical and Electronics Engineering

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BASIC ELECTRICITY AND NETWORK THEOREMS  OHM’S LAW: Ohm’s law states this relationship in simple words ‘‘the current flowing circuit (I) is directly proportional to applied voltage (V) provided resistance in the circuit is constant ’’  IαV or VαI 1.Resistance =

Voltage V OR R= Current I

2.Voltage=Current×Resistance OR V= I×R

3.Current 

Voltage V OR I  Resistance R

 VOLTAGE: Voltage is necessary to set up the current flow. Voltage is also known as '' potential difference '', '' EMF '' In actual practice voltage source is of two types 1. AC Voltage (Alternating Current type) 2. DC voltage (Direct Current type)

 CURRENT: An electric current through a conductor is a flow of electrons; actually electric charge in motion is called as current.

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 Conventional Current: The electron flow is always from-Ve terminal to +Ve terminal of the battery but theoretically it is assumed to be from positive to negative, because as a convention, electric current direction a conventional current from positive to negative.

Electron Flow & conventional current

ď ś SOURCES OF ELECTRICITY: i) AC Source and ii) DC Source i) AC Source: a) Signal generator: If can generate AC supply with variable voltage and variable frequency, sometimes, they are capable of generating different AC signal with different waveforms like square wave, triangular wave, sawtooth etc.

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b) Alternator: It is a sort of generator can generate AC supply converting mechanical energy into electrical energy. E.g. in auditorium when MSEB fails they start generators or while in festivals or Circus owner they use their self-generators. ď ś DC SOURCES: We get AC supply from main electric power station but most of the electronic circuits work on DC supply, user has to take DC supply from the following sources i) Batteries ii) DC generators iii) Rectifiers iv) solar cell The battery is a very common DC source because of its high current capacity and recharging facility. It can be recharged for many times; now a day in automobile applications it is continuously charged by electronic circuits when engine starts. A battery is a unit in which no. of cell are arranged in series and parallel arrangement.

The DC generator is a dynamic engine it generates DC energy by means of rotating shaft it generates electrical energy by converting mechanical energy.

A rectifier is an electronic instrument which converts mains AC supply into DC there is no rotating part. ď ś IDEAL AND PRACTICAL VOLTAGE SOURCE: Ideal voltage source is not possible; the source cannot maintain source voltage at its terminals it would mean that it could supply an infinite power to a load even if the circuit is a short circuit.

A practical voltage source is the true source it is a source with small internal impedance as indicated by fig. There I-V characteristics show that as load current increases its terminal voltage decreases due to drop across its internal impedance.

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 IDEAL AND PRACTICAL CURRENT SOURCE: A current source can be a source, which can deliver constant current even if load varies from low to high value.

It is a quite similar concept of ideal current source, where it supplies constant current (I) even current through load varies. It means that even if the circuit is an open circuit practically current flow is not possible. On the other hand a practical current source is represented by a current source with internal impedance in parallel with source. It can be stated that a good current source has high internal impedance so that very small current is passed through it and almost constant current flows through the load. As shown in the fig Z=Zi parallel ZL Z=ZL when ZL =0 or Zi= 

 Comparison: Voltage source It is voltage with minimum internal impedance.

Current source It is voltage with maximum internal impedance.

It is a voltage source in series with Zi

It is a voltage source in parallel with Zi

It works when ZL>>Zi

It works when Zi>>ZL

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CONTACT: 9821131002/9029004242 IMPORTANT FORMULAE

1. Rt=R1+R2+R3+……….Series circuit 1 1 1 1 2. R  R  R  R ……..Parallel circuit T 1 2 3 3. When R1 and R2 are in series across a supply V then voltage across R2 By voltage divider formula

VR 2 

R2 X V R1  R2

4. When R1 and R2 are in parallel then the current through R2 by current divider formula

I2 

R1 X IT R1  R2

I1 

R2 X IT R1  R2

 POWER: Power is defined, as ‘‘it is the rate of doing electric work ‘’.

P

 W /t

But V  W / Q W  V  Q and I   Q / t  Q / I Substituting these two VQ P  V  I Q/I P V  I (Watts  Volts  Amp) Substituting V  IR in equation (1) P  ( IR)  I P

I2 R

............(1)

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

Now we can make one more relation by substituting (I=V/R) in equation (1) P  V  (V / R)

P



V2 R

...........(3)

Formulae: (1) P  V  I

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(2) P  I 2 R

(3) P 

5

V2 R

Basic Electricity & Network Theorems

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 KIRCHHOFF’S LAWS: (1) Kirchhoff’s current law (KCL): It states that ‘‘The algebraic sum of currents at any junction or node is always zero’’. Where currents coming towards node are considered with positive sign and currents leaving the node are considered with negative sign.

As shown in fig. the equation for node will be I1  I 2  I3  I 4  0

(2) Kirchhoff’s voltage law (KVL): It states that ‘‘The algebraic sum of voltages around any closed loop is always zero.’’ Here loop means a closed circuit path. Kirchhoff’s equation can be written as V1  V2  V3  V or V  V1  V2  V3.  SUPERPOSITION THEOREM: Statement: ‘‘In a network containing two or more sources, the current or voltage for any component is the algebraic of the results produced by each source acting individual source’’.

Example 1: Find the P.D. between point A and B

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Solution: Step-I Make V2 short and find VAB across R2 say (V1)

By Voltage divider formula R2 Va   V1 R1  R2 Va 

6K  24  16V 9K

Step-II Now make V1 short and find VAB across R1 say (V2) R1 Vb   V2 R1  R2 3 Vb   9  3V 9

Example 2: Find current through R3 if R3  1K 

 Step-I Make V2 short & find voltage across R2 (say Va )

12 x 30  20V 18  Step- II Make V1 short and find voltage across R1 (Say Vb ) Va 

Vb 

V2 x R1 30 x 6  R1  R2 18

 10 V  Step-III Apply Superposition VAB  Va  Vb = 20+10 =30V The current through R3 

VAB 30   30 103  30mA 3 R3 110

Drawback of superposition theorem: it is suitable only when the network contains linear components.

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 THEVENIN’S THEOREM:

Statement: Any linear active, resistive complex network containing one or more sources can be replaced by an equivalent voltage source (Veq) and a series equivalent resistance (Req).

Where (Veq) or ( VTH ) = The venin’s equivalent voltage source And

(Re q) or ( RTH ) = Thevenin’s Equivalent resistance

 NORTON’S THEOREM:

Statement: Any linear active, resistive complex network containing one or more sources can be replaced by an equivalent current source (Ieq) and a parallel equivalent resistance (Req).

Where And

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( Ieq) or ( I N ) = Norton’s equivalent current source (Re q) or ( RN ) = Norton’s Equivalent resistance

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 COMPARISON OF THEVENIN’S WITH NORTON’S THEOREM: Thevenin’s Theorem

Norton’s Theorem

1. It is used when a complex network contains one or many voltage sources.

1. It is used when a complex network contains one or many current sources

2. Mostly used in analysis voltage.

2. Mostly used in analysis of current

3. It has a single equivalent voltage source (Veq) when terminals are open circuited.

3. It has a single equivalent current source (Ieq) when terminals are short circuited.

4. The Thevenins equivalent resistace (Req) is in series with Veq. 5. Thevenin’s Equivalent circuit

4. Req is in parallel with Ieq. 5. Norton’s Equivalent circuit

 Example 1: Draw Thevenin’s equivalent circuit and find voltage across ‘RL’.

Step (I) Make terminal AB open and find Veq

VR 2  Veq 

Step (II) Make terminal AB open and find Veq

VxR2 R1  R2

VR 2  Veq 

6 x12  4V 18 (Note that R3 is open hence VR2 is Veq) 

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

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VxR2 R1  R2 6 x10  6.66V 9

Basic Electricity & Network Theorems

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Step (II) Find Req by making source short

Re q 



R1 x R2 R1  R2

Re q 

6 x12  4 18



Step (III) Draw Thevenine’s equivalent circuit & find VL

VR 2 



R1 x R2  R3 R1  R2 6 x3  3  5 9

Step (III) Draw Thevenine’s equivalent circuit & find VL

Veq x RL Re q  RL

VR 2 

4x6  2.4V 10



Veq x RL Re q  RL 6.6 x 3  2.4975V 8

 Example 2: Find Current through the load and voltage across the load by Norton’s theorem in the given circuit.

Solution: Step (I) Make output terminals short and find short find short circuit current Ieq.

Note: that 20 Ω resistance becomes short or 0 Ω J Electronic cs - I

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Step (II) Make voltage source short and find Req.

Step (III) Draw Norton’s equivalent circuit and find IL and VL.

It can be verified by Thevenin’s equivalent circuit.

Step (I) Find Veq by making AB open

Step (II) Find Req or use Req from Norton’s method and find VL by voltage divider formula.

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 Example 3: Find VL and IL by Norton’s & Thevenin’s Theorem.

Solution: Applying Norton’s Theorem Step (I) Make the output terminals short and find short circuit current Ieq.

Step (II) Make source voltage short and find Req.

Step (III) Draw Norton’s equivalent circuit and find IL and VL

It can be verified by Thevenin’s equivalent circuit.

Step (I) Find Veq by making AB open

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 Example 4: Find VL and IL by using both Norton’s & Thevenin’s Theorems.

Solution: (A) Applying Norton’s Theorem Step (I) Make the output terminals short and find short-circuit current Ieq.

Step (II) Make the source voltage short and find Req.

Step (III) Draw Norton’s equivalent circuit and find IL

It can be verified by Thevenin’s equivalent circuit.

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(B) Applying Thevenin’s Theorem Step (I) Find Veq by making AB open. Veq is nothing but voltage across R2 because AB is open.

 MAXIMUM POWER TRANSFER THEOREM: ‘’The maximum power transfer takes place when the load resistance ( R1 ) is equal to the to the equivalent source resistance (Req)’’.  Comparison Of Electric And Magnetic Field: Electric circuit

Magnetic circuit

1.

1.

Magnetic system results in flux.

Electric field results in electron flow 2. Flow of electron is current.

2. Flow of flux.

3. The cause of current is E.M.F. (Voltage)

3. The cause of flux is M.M.F Magneto Motive Force.

4. Opposition to the flow of electron is known as resistance (R) 5. Resistance is given by R= σ1 A where

4. Opposition to the flow is known as reluctance (R) 5. Reluctance is given by R=1 μ

 is the conductivity.

7. Ohms law = V I

where  is the permeability.

1R 6. Permanence= 7. Reluctance R=MMF/ 

8. Current in an electric circuit is due to electron flow.

8. Flux in magnetic circuit does not actually flow.

9. Magnetic field is generated when curre3nt flows through a conductor.

9. Electricity can be generated by magnetic field.

10. Energy is required to maintain the current in the

10. Energy is required only to create flux but not no maintain it.

6. Conductance =

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Basic Electricity & Network Theorems

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 ELECTROMAGNETISM: Magnetic field is always produced around the conductor, when electric current flows through it. This phenomenon can be observed by performing simple experiment as shown in fig….

Shown that when current flows through the conductor iron filings are aligned in concentric rings around the conductor; this shows that magnetic field is developed in circular orbits around the conductor. Another important conclusion is, iron filings are dense near to the conductor that is magnetic field is strongest neat the conductor and it decreases with increase in distance. Third conclusion is- higher is the current flow higher is the magnetic field. Magnetic force of lines is known as ‘‘magnetic flux ()’’ and the number of magnetic lines of force that pass through the unit area of a section perpendicular to the direction of the magnetic flux is known as ‘‘ flux density ’’.  ELECTROMAGNETIC INDUCTION: Electrons in motion (current) produce a magnetic field, similarly when magnetic flux moves, it forces free electrons in conductor to move, which produce an electric current.

Shows the conductor AB is placed at right angles to the flux produced by the magnet.

When magnet is moved up and down, the conductor cuts the lines of magnetic flux.

Therefore whenever the conductor cuts flux current is produced in the conductor. This current is observed in micrometer as shown. When magnet is moved downward, current flows from A to B and when it moves upward, current flows in opposite direction.

If you move conductor AB instead of magnet then also induction can be observed because the conductor cuts magnetic flux. Hence whenever either flux is in motion or conductor is in motion electricity is produced in the conductor by induction. Same principle is used in an electric generator.

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 INDUCTANCE: It is the ability of conductor induced voltage, when current through it varies. Induced voltage is the result of flux cutting across a conductor because when ac current flows through it magnetic flux varies its strength and the direction, which is equivalent to motion of magnetic flux.  FARADAY’S LAW: When a conductor cuts the line of magnetic field (flux) an e.m.f. is generated in the conductor or when magnetic flux is made varying across the conductor an e.m.f. can be generated in the conductor.

The voltage induced by induction depends upon the following three factors: 1) Amount of Flux () : Higher is the number of magnetic lines of force (or magnetic flux) higher will be the induced voltage.

2) Number of Turns (N): The more turns in a coil the higher is induced voltage, because induced voltage is the sum of individual voltages generated in each turn of the coil.

3) Faster the rate of cutting flux, higher is the induced voltage.  SELF INDUCTANCE AND MUTUAL INDUCTANCE: The ability of a conductor to induce voltage in itself when the current changes through it, is known as its ‘‘ Self inductance’’ or simply inductance. The notation of inductance is ‘L’ and it is measured in ‘Henry’. This induced voltage has a tendency to oppose change in current. Therefore induced voltage is often called as ‘‘counter emf’’ or ‘‘back emf’’.

When current through coil is AC and if voltage is induced in itself it is called as its ‘self-inductance’.

But when AC current flows through one coil and voltage is induced in other coil placed near to it then it is known as ‘mutual inductance’.

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