What is Alternator?

                     What is Alternator? 

An alternating current generator is called alternator. It works on the principle of
electromagnetic induction. An alternator is also called as AC Generator or synchronous generator.

Working principle of alternator:

An alternator works on the principle of faraday’s law of electromagnetic induction. It
states that when there is a relative motion between magnetic field and a conductor an e.m.f is induced in the conductor.
Alternating voltages / current may be generated by two ways:

•  By rotating a coil in a magnetic field.
•  By rotating a magnetic field within a stationary coil.

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The quantity of voltages / current generated depends upon:

• The number of turns in the coil.
• Strength of the magnetic field 
• The speed at which the coil of magnetic fields rotates.

 It is seen that the induced E.M.F. varies as sine function of the time angle t. This curve is
known as sine wave and the E.M.F which varies in this manner is known as sinusoidal E.M.F.
e = Em sin ωt
Where, e = Instantaneous voltage
Em = Maximum voltage
ωt = Angular velocity of the coil

What is Star to Delta Conversion?

What is Star to Delta Conversion? 

                            R12 R31

We know, R1 =------------------------           ---------- (1)
                         R12 + R23 +R31     

          R23 R12
R2 =----------------------------                      ---------- (2)
        R12 + R23 +R31


         R31 R23
R3 =-----------------------------                       ---------- (3)
         R12 + R23 +R31

From the above relations:

                                    R12 2R23 R31
(1) X (2) => R1 R2 =---------------------------    ---------- (4)
                                    R12 + R23 +R31


                                     R12 R23 2 R31
(2) X (3) => R2 R3 =-----------------------------     ---------- (5)
                                     R12 + R23 +R31


                                    R12 R23 R31 2
(3) X (1) => R3 R1 =----------------------------      ---------- (6)
                                    R12 + R23 +R31

By adding Equation: (4) + (5) + (6)


                                          R12 R23 R31 (R12 + R23 +R31)
R1 R2 + R2 R3+R3 R1 =--------------------------------------------
                                             (R12 + R23 +R31)2

                  R12 R23 R31
              =--------------------------
                 R12 + R23 +R31

                R23 R31
    R12 =---------------------------  x (R1 R2 + R2 R3+R3 R1)
              R12 + R23 +R31


               R1 R2 + R2 R3+R3 R1
   R12 =---------------------------------------
                                R3


               R1 R2 + R2 R3+R3 R1
   R23 =-----------------------------------------
                               R1


               R1 R2 + R2 R3+R3 R1
   R31 =--------------------------------------
                               R2

What is Delta to Star Conversion?

What is Delta to Star Conversion? 

Consider a three terminal network in which the resistors are connected in the form ∆.
Such a network is known as delta network. Let the resistor values are R12, R23 and R31. Now we
find its equivalent Y-network such that both the circuits are identical as far as the terminals 1,
2 and 3 are concerned. Let the resistor values are R1, R2 and R3.

In Delta (Δ) Connection: 

                                                                    R12(R23 + R31)

Equivalent Resistance between 1 &2 =--------------------
                                                                    R12 + R23 +R31

In Star (Y) Connection: 

Equivalent Resistance between 1 &2 = R1 + R2
Resistance between terminal 1 & 2 in Y = Resistance between terminal 1 & 2 in Δ
delta

                  R12(R23 + R31)
R1 + R2 =----------------------------               --------------- (1)
                  R12 + R23 +R31


                                   R23(R31 + R12)
Similarly, R2 + R3 =---------------------------    ---------- (2)
                                   R12 + R23 +R31

                   R31(R12 + R23)
R3 + R1 =---------------------------                     ---------- (3)
                   R12 + R23 +R31

Subtract Equation (2) from Equation (3):


                   (R12R31 + R23R31 − R23R31 − R12R23)
R1 − R2 =------------------------------------------------------------------
                                     R12 + R23 +R31

                   R12(R31 − R23 )
R1 − R2 =-----------------------------              ---------- (4)
                   R12 + R23 +R31

Add Equation (1) and Equation (4):

            2 R12 R31
2R1 =---------------------------
          R12 + R23 +R31

          R12 R31
R1 =----------------------------
          R12 + R23 +R31


                           R23 R12
Similarly, R2 =------------------------------
                           R12 + R23 +R31

          R31 R23
R3 =------------------------------
          R12 + R23 +R31

What is Maximum Power Transfer Theorem?

What is Norton’s Theorem?

What is Norton’s Theorem? 

Norton’s theorem is a method for simplifying a two terminal linear circuit to an
equivalent circuit with only a current source in parallel with a resistor. This basic difference
between Thevenin’s Theorem and Norton’s theorem is that, Norton’s theorem results in an
equivalent source in parallel with an equivalent resistance. The equivalent current source is
designated IN, and the equivalent resistance is designated RN. To apply Norton’s theorem, you
must know how to find the two quantities IN and RN.

Statement:

Norton's theorem states that any two terminal network can be replaced by a single
current source IN in parallel with a single resistance RN.

Procedure:

i) Remove the load resistance RL and put a short circuit across terminals.
ii) Find the short circuit current (IN or ISc)
iii) Find the equivalent resistance RN as seen from open circuited terminals by replacing
the voltage source by its internal resistance.
iv) Draw the Norton’s equivalent circuit by a current ISC in series with the equivalent
resistance Rth or RN
v) Find the current through RL by applying current divider rule.

       IN x RN

IL =--------------
        RN + RL

Explanation: 

Step 1: Remove the Load Resistor (RL) and Short circuit its terminals.

Step 2: Find Short Circuit Current or Norton’s Current (ISC or IN)
ISC or IN = Current through branch A and B
ISC or IN = I3

                                                               R2 x R3
Equivalent Resistance Req = R1 + (----------------)
                                                               R2 + R3

                      E
Current I1 =------
                     Req

Current through Shorted path(ISCor IN) = I3

                          I1 x R2
So, ISCor IN =---------------
                          R2 + R3

Step 3: Find RN (Equivalent Resistance between Terminal A and B)

          R1 x R2
R12 =--------------
          R1 + R2

RN = R12 + R3

Step 4: Draw Norton’s equivalent circuit

Step 5: Find the Load Current (IL):

       IN x RN
IL =-------------
       RN + RL

What is Thevenin’s theorem?

What is Thevenin’s theorem? 

Thevenin’s theorem provides a method for simplifying a circuit to a standard equivalent
form. This theorem can be used to simplify the analysis of complex circuits.
Statement:
Any linear bilateral network may be reduced to a simplified two-terminal circuit
consisting of a single voltage source (Vth) in series with a single resistor (Rth)
Procedure:
i) Remove the load resistance RL and put an open circuit across terminals.
ii) Find the voltage across open circuited terminals (Vth or Voc)
iii) Find the equivalent resistance Rth as seen from open circuited terminals by replacing
the voltage source by its internal resistance.
iv) Draw the thevenin’s equivalent circuit by a voltage Vth in series with the equivalent
resistance Rth

Find the current through RL by applying ohms law.
Explanation:
            Vth
IL = ----------------
        Rth + RL

Step 1: Open Circuit the Load Resistor (RL)

Step 2: Find Open Circuit Voltage (Vth)
Vth = P.D across terminals A
and B P.D across terminals A and B = P.D across R2 Resistor
                                        Vth = I x R2
                                             E
                                     I = ------------
                                        (R1 + R2)

                E. R2

       Vth = ------------------------

                     (R1 + R2) 

Step 3: Find Thevenin’s equivalent Resistance: Rth
                             
                                     R1 x R2
                           R12 =---------------
                                     R1 + R2
               
                            Rth = R12 + R3

Step 4: Draw Thevenin’s equivalent circuit

Step 5: Find the Load Current (IL):

                                       Vth
                             IL =--------------
                                    Rth + RL

What is Kirchhoff’s laws?

What is Kirchhoff’s laws? 

Kirchhoff’s laws are more comprehensive than ohm’s law and are used for solving
electrical networks.
The two Kirchhoff’s laws are:
1. Kirchhoff’s Current Law (KCL)
2. Kirchhoff’s Voltage Law (KVL)
Kirchhoff’s Current Law (KCL)
It states that “the algebraic sum of the currents in a junction of a circuit is zero.
(or)
The sum of current entering the junction is equal to the sum of the current leaving
the junction.
Explanation:
Consider 5 conductors carrying currents. Assume positive sign for the current flowing
towards the junction and negative sign for the current flowing away from the junction.
Let P is a junction
I1, I3, & I4 = incoming current towards the junction P
I2, & I5 = outgoing current away from the junction P
By applying Kirchhoff ’ s current law at junction P,
 I1 - I2 + I3 + I4 - I5 = 0
 I1 + I3 + I4 = I2 + I5
Sum of incoming current = sum of outgoing
current

Kirchhoff’s Voltage Law (KVL):

It states that in any closed electrical circuit, “the algebraic sum of voltage is zero”.
(OR)
That is the sum of voltage rises (EMF) in a closed network is equal to the sum of
voltages drops (P.D)

Explanation:

Consider a simple closed electrical circuit,
Let,
 E - Supply voltage
 R1, R2 & R3 - Resistors in the circuit.
 I - Current flow through the circuit
 V1 – p.d across R1
 V2 – p.d across R2
 V3 – p.d across R3
Applying Kirchhoff’s voltage law to the closed circuit,
 E - V1 - V2 - V3 = 0
 E = V1+V2+V3 ----------- (1)
 Substitute, V1 = I.R1, V2 = I.R2 & V3 = I.R3 in equation (1)
 E = IR1+IR2+IR3
 E - IR1 - IR2 - IR3 = 0 [Algebraic sum of voltages is zero]