WHAT HAPPENS WHEN TRANSFORMER IS AT NO-LOAD?

Phasor Diagram At No Load

Phasor diagram for a transformer(real) under no-load condition is shown in the fig. below.

Iw = I0 . cos(0).

Im = I0 . cos(0)

I0 = v{(Iw) + (Im)}

Since, E1 and E2 are induced by the same flux ?, therefore E1 and E2 will be in same phase , but E1 and E2 lags behind the flux ? by 90 degree. E1 = k. E2 (where k = T1/T2,  T1 & T2 are no. of turns on primary and secondary winding)

E1 and V1 will be opposite to each other due to Lenz Law. If the voltage drop in the primary winding are neglected then V1 will be equal and opposite to the E1.

Power input to the transformer during no-load condition is :-

P0 = V1 . I0. cos (0)

In this article we will study about h-Parameter of two port network.

h-Parameter representation is widely used in modelling of electronic components and circuits, particularly transistors.

h-Parameter is called "Hybrid Parameter".

In h-Parameter, the input voltage and output current are function of input current and output voltage respectively.

Y-Parameter is also called "Short Circuit Parameter" and "Admittance Parameter".
In Y-Parameter, the input and output currents are function of input and output Voltages.
( I1 , I2 ) = f ( V1 , V2 )
It can also be written as:
[I] = [Y]   [V]
where [Y] represents Admittance Matrix.
In matrix form,
[I1] =    [Y11  Y12]   [V1]
[I2] =    [Y21  Y22]   [V2]
Writing it in equation,
I1 = Y11* V1 + Y12* V2 .........eq1
I2 = Y21* V1 + Y22* V2 .........eq2
CASE-1 SHORT CIRCUITING THE OUTPUT PORT
If the Output port of the two port network is  short circuited then output voltage is zero, i.e. V2 = 0.
Now, equation 1 and 2 will be reduced to :
I1 = Y11* V1
I2 = Y21* V1
So, Y11 = I1 /V1    ( keeping v2 = 0 )
      Y21 = I2/ V1    ( keeping V2 = 0 )
CASE-2 SHORT CIRCUITING THE INPUT PORT
If the Input port of the two port network is short circuited then the input voltage is zero, i.e. V1 = 0.
Now, equation 1 and 2 will be reduced to :
I1 = Y12* V2
I2 = Y22* V2
So, Y12 = I1/ V2    ( keeping V1= 0 )
       Y22 = I2/ V2  ( keeping V1 = 0 )
Y11 is called input driving point Admittance.
Y12 is called forward transfer Admittance.
Y21 is called reverse transfer Admittance
Y22 is called output driving point Admittance.
For a network to be symmetrical , Y11 = Y22
For a network to be reciprocal, Y12 = Y21
EQUIVALENT CIRCUIT OF Y-PARAMETER

Z-Parameter is also called "Open Circuit Parameter" and "Impedance Parameter".
In Z-Parameter, the input and output voltage are function of input and output current.
( V1 , V2 ) = f ( I1 , I2 )
It can also be written as:
[V] = [Z][I]
Where Z represents Impedance Matrix.
In matrix form
[V1] =    [Z11  Z12]   [I1]
[V2] =    [Z21  Z22]   [I2]
Writing it in equation,
V1 = Z11* I1 + Z12* I2 .........eq1
V2 = Z21* I1 + Z22* I2 .........eq2
CASE-1 OPEN CIRCUITING THE OUTPUT PORT
If the Output port of the two port network is open circuited then the output current is zero, i.e. I2 = 0.
Now, equation 1 and 2 will be reduced to :
V1 = Z11* I1
V2 = Z21* I1
So, Z11 = V1/ I1    ( keeping I2 = 0 )
Z21 = V2/ I1  ( keeping I2 = 0 )
CASE-2 OPEN CIRCUITING THE INPUT PORT
If the Input port of the two port network is open circuited then the input current is zero, i.e. I1 = 0.
Now, equation 1 and 2 will be reduced to :
V1 = Z12* I2
V2 = Z22* I2
So, Z12 = V1/ I2    ( keeping I1 = 0 )
Z22 = V2/ I2  ( keeping I1 = 0 )
Z11 is called input driving point Impedance
Z12 is called forward transfer Impedance
Z21 is called reverse transfer Impedance
Z22 is called output driving point Impedance.
For a network to be symmetrical , Z11 = Z22
For a network to be reciprocal, Z12 = Z21
EQUIVALENT CIRCUIT OF Z-PARAMETER

In this case, a external resistance Re is connected in the armature circuit of the dc series motor. When the value of the external resistance is increased, it will cause increased voltage drop. Hence the effective voltage across the armature circuit will be reduced.

Speed will also reduced. So the speed of the motor can be controlled by varying the resistance.  As the value of Re is increased then motor will run at lower speed.

In this method , a variable resistance called diverter, Rd is connected in parallel across the series field winding. This resistance reduces the current flowing through the series field winding and it results in lesser field flux. Since the speed is inversely proportional to the field flux , so the speed of the motor will increase.

If the value of diverter resistance is decreased then more current will flow through it instead of series field winding and lesser flux will produce which will increase the speed of the motor.

This can also be achieved by providing a tapped series field winding, which is most commonly used for traction purposes.

In this article we will study about the Hot Wire Instruments, it construction , working , advantages and disadvantages.

These type of instruments are mainly used as Ammeter but can be used as Voltmeter by connecting a high resistance in series.

As shown in the figure , this type of instrument consists of a wire AB which is made up of platinum-iridium because it can withstand oxidation at higher temperature. Wire AB is stretched between a fixed end B and adjusting screw at A. When current is to be measured , it is then passed through the wire AB.

There is a another wire CD which is usually made up of phosphor-bronze. One end of wire CD is is attached to the center of AB while other end of CD is taken over the pulley by silk thread. This silk thread is pulled by the spring S.

Working principle of hot wire instrument is based upon the heating effect of Electric Current. When the current is passed through the wire AB , it expands. This produces the sag in wire AB , since the wire CD is attached to AB. So it will produce a slack in CD, this slack in CD is taken up by the silk thread which after passing through the pulley is attached to the spring. As soon as the silk thread is pulled by the spring, the pulley moves , therefore produces a deflection in the pointer which in turn gives the reading on calibrated scale.

It can be seen that the deflection of the pointer is proportional to the extension of wire AB which is proportional to the  square of the current (I(2)).

Damping :  Generally eddy current damping is provided in hot wire instrument. A thin light aluminium disc is attached to the pulley such that it moves between the poles of permanent damping magnet ,M.