SSC JE Electrical Conventional Paper Solved 2014-Electrical-Exam

Ques 2(a).  What do you mean by Magnetic Hysteresis? Differentiate between Hard and soft Magnetic materials.

Answer:- Hysteresis is the heart of the behavior of magnetic materials. All applications, from electric motors to transformers and permanent magnets, from various types of electronic devices to magnetic recording, depend heavily on particular aspects of hysteresis.

MAGNETIC HYSTERESIS

When a magnetic material is magnetized first in one direction and then in the other (i.e., one cycle of magnetization), it is found that flux density B in the material lags behind the applied magnetizing force H. This phenomenon is known as magnetic hysteresis.

Hence, the phenomenon of flux density B lagging behind the magnetizing force H in a magnetic material is called magnetic hysteresis.

‘Hysteresis’ is the term derived from the Greek word hysterein, meaning to lag behind. To understand the complete phenomenon of magnetic hysteresis, consider a ring of magnetic material on which a solenoid is wound uniformly as shown in Figure (a). The solenoid is connected to a DC source through a double pole double throw reversing switch (position ‘1’).

Hysteresis loop

When the field intensity H is increased gradually by increasing current in the solenoid (by decreasing the value of R), the flux density B also increases until saturation point a is reached and curve so obtained is oa. Now, if the magnetizing force is gradually reduced to zero by decreasing the current in the solenoid to zero, the flux density does not become zero and the curve so obtained is ah, as shown in Figure(b). When magnetizing force H is zero, the flux density still has value ob.

Residual Magnetism and Retentivity

This value of flux density ‘ob’ retained by the magnetic material is called residual magnetism and the power of retaining this residual magnetism is called retentivity of the material. To demagnetize the magnetic ring, the magnetizing force H is reversed by reversing the direction of flow of current in the solenoid. This is achieved by changing the position of double pole, double throw switch (i.e., position ‘2’). When H is increased in reverse direction, the flux density starts decreasing and becomes zero and curve follows the path be. Thus, the residual magnetism of the magnetic material is removed by applying magnetizing force oc in opposite direction.

Coercive Force

This value of magnetizing force oc required to remove the residual magnetism is called coercive force. To complete the loop, the magnetizing force H is increased further in reverse direction till saturation reaches (point ‘d’) and the curve follows the path cd. Again H is reduced to zero and the curve follows the path de, where oe represents the residual magnetism. Then, H is increased in the positive direction by changing the position of the reversible switch to position ‘ 1’ and increasing the flow of current in the solenoid. The curve follows the path of efa and the loop is completed. Again of is the magnetizing force utilized to remove the residual magnetism oe.

Hence, cf is the total coercive force required in one cycle of magnetization to remove the residual magnetism. Since the meaning of hysteresis is lagging behind, and in this case, flux density B always lags behind the magnetizing force, H. Therefore, loop (abcdefa) so obtained is called hysteresis loop.

Soft and Hard Magnetic Materials

The process of magnetization of a ferromagnetic material consists of moving the domain walls so that favorably oriented domains grow and unfavorably oriented domains shrink,

  • If the domain walls are easy to move, the coercive field is low, it is easy to magnetize the material, Such a material is called a soft magnetic material.
  • If it is difficult to move the domain walls, the coercive field is large and the material is magnetically hard.

Fig.shows magnetization curves for soft and hard magnetic materials.

Soft Hard Hysteresis loop

Soft Magnetic Materials

Fig. 47.5 shows the nature of hysteresis loop of soft magnetic material, (soft iron).The soft magnetic material has a narrow magnetic hysteresis loop as shown in the figure below which has a small amount of dissipated energy. 

soft Iron

  • Soft magnetic materials have low hysteresis loss due to smaller hysteresis loop area.
  • In these materials, the domain wall movement is relatively easier Even for small changes in the magnetizing field, magnetization changes large amounts.
  • The coercivity and retentivity are small. Hence these materials can easily magnetized and demagnetized.
  • Soft magnetic materials are used in applications requiring frequent reversals of the directions of magnetization such as cores of transformers.
  • In soft magnetic materials, the hysteresis losses must be kept down to a minimum. When the magnetic induction is large for a small applied field, the loop area is small and the hysteresis loss is reduced. The key factor in the design of a soft magnet is then lo have easily moving domain overalls. Soft magnetic materials should be free of impurities and inclusions.
  • The other source of energy loss in soft magnetic materials is the eddy current loss (changing magnetic flux in a medium induces an emf). The induced emf is proportional to the rate of change of flux and hence to the frequency of the alternating current. The induced emf sets up eddy current. The power loss due to these is equal to V2/R. Here, V is the induced emf and R is the resistance of the medium. Eddy current losses can be minimized by increasing the resistivity of the medium.
  • Soft Magnetic Material has high Susceptibility and Permeability.
  • The Magnetic energy stored is Low.
  • The material which is used to make soft Magnetic Materials are iron, silicon steel, etc.
  • They are suitable for making Transformer core, electromagnets etc.

Hard Magnetic Materials

Fig.shows the nature of hysteresis loop of hard magnetic material (steel).The Hard magnetic material has a wider hysteresis loop as shown in the figure below and results in a large amount of energy dissipation and the demagnetization process is more difficult to achieve.

Hard Iron

  • Hard magnetic materials have large hysteresis loss due to larger hysteresis loop area.
  • in these materials, the domain wall movement is difficult because of the presence of impurities and crystal imperfections and it is irreversible in nature.
  • The coercivity and retentivity are large. Hence, these materials cannot be easily magnetized and demagnetizer
  • Hard magnetic materials are used to produce permanent magnet.
  • Hard Magnetic Material has Low Susceptibility and Permeability.
  • Magnetic Energy Stored is High.
  • The eddy current losses are high.
  • They are suitable for making permanent magnet e.g Alnico

Ques 2(b). Deduce an expression for the average power in a single phase RL circuit hence explain the term power factor.

Answer:- 

Consider the R-L-circuit as shown in the figure. Let V be the source voltage phasor, I the current phasor, VR, and VL the phasor voltage drops across the resistor and inductor respectively. As we know that the voltage drop across the inductor leads the current through it by 90° and in a resistor, the voltage and current are in phase.

RL Circuit

Generally, to draw the phasor diagram of series circuits, the current is taken as the reference phasor and various voltage drops plotted in correct phase with respect to current. In Figure I is the reference, VR is in phase (parallel) with it, VL is plotted leading it by 90°. The source voltage is the phasor sum of VR and VL.

Average power in a single phase RL circuit

In RL circuit in which the current leads the voltage by an angle φ.This condition occurs when the voltage across the capacitor is more than the voltage across the inductor. Therefore

The Instantaneous voltage applied is given as

V = Vm sinωt

where Vm = is the maximum voltage or voltage amplitude

ω = angular frequency

I = Im sin(ωt − φ)

As in DC circuits, the instantaneous electric power in an AC circuit is given by

P = VI

P = Vm sinωt × Im sin(ωt − φ)

P = VmIm sinωt . sin(ωt − φ)

Multiplying and dividing the above equation by 2 we get and as we know that 
2sinA.sinB = cos(A − B) − cos(A + B)

[latex display=”true”]\begin{array}{l}P = \dfrac{{{V_m}{{\mathop{\rm I}\nolimits} _m}}}{2}2\sin \omega t.\sin (\omega t – \Phi )\\\\ = \dfrac{{{V_m}{{\mathop{\rm I}\nolimits} _m}}}{2}\left[ {\cos (\omega t – \omega t – \Phi ) – \cos (\omega t + \omega t – \Phi )} \right]\\\\ = \dfrac{{{V_m}{{\mathop{\rm I}\nolimits} _m}}}{2}\left[ {\cos \Phi – \cos (2\omega t – \Phi )} \right]\end{array}[/latex]

Now as we know that the average of all the instantaneous values of an alternating voltage and currents over one complete cycle is called Average Value. e.g sinωt, cosωt, cos2ωt , cos(2ωt + φ) etc.

If we consider symmetrical waves like sinusoidal current or voltage waveform, the positive half cycle will be exactly equal to negative half cycle.

Hence it is clear that the second terms of the above equation i.e cos(2ωt + φ) = 0

[latex display=”true”]\begin{array}{l}P = \dfrac{{{V_m}{{\mathop{\rm I}\nolimits} _m}}}{2}\left[ {\cos \Phi } \right]\\\\P = \dfrac{{{V_m}}}{{\sqrt 2 }}\dfrac{{{{\mathop{\rm I}\nolimits} _m}}}{{\sqrt 2 }}\left[ {\cos \Phi } \right]\\\\\dfrac{{{V_m}}}{{\sqrt 2 }} = {V_{RMS}}\\\\\dfrac{{{{\mathop{\rm I}\nolimits} _m}}}{{\sqrt 2 }} = {I_{RMS}}\\\\P = {V_{RMS}}{I_{RMS}}\cos \Phi \\\\or\\\\P = VI\cos \Phi \end{array}[/latex]

Power factor

There are many ways to understand POWER FACTOR

⇒ One definition expresses power factor as the cosine of the phase displacement angle between the circuit voltage and current.

CosΦ = V/I

⇒The other definition is that power factor is the ratio of active power to apparent power in a circuit. It is generally given in percent. Most utilization devices require two components of current, active and reactive. The power-producing current (active current) is the current that is converted by the equipment into work, usually in the form of heat, light, or mechanical power. The unit of active power is the watt. The magnetizing current (reactive current) is the current required to produce the flux necessary to the operation of electromagnetic devices. The unit of reactive power is the var.

power factor triangle

[latex]{\text{Power Factor = }}\frac{{{\text{True power}}}}{{{\text{Apparent Power}}}}[/latex]

⇒  Power factor can also be described as the degree at which given load matches with resistive load”.

In the case of sinusoidal sources, the power factor is the cosine of the phase angle between voltage and current

Power Factor = cosθ

As the phase angle between voltage and total current increases, the power factor decreases. The smaller the power factor, the smaller the power dissipation. The power factor varies from O to 1. For purely resistive circuits, the phase angle between voltage and current is zero, and hence the power factor is unity. For purely reactive circuits, the phase angle between voltage and current is 90°, and hence the power factor is zero. In an RC circuit, the power factor is referred to as leading power factor because the current leads the voltage. In an RL circuit, the power factor is referred to as lagging power factor because of the current lags behind the voltage.

Unit of Power Factor

Power factor is a dimensionless number in the closed interval of −1 to 1.

High and Low Power factor

Poor power factor has many disadvantages:

  1. The degraded efficiency of distribution power systems
  2. Decreased capacity of transmission, substation, and distribution systems.
  3. poor voltage regulation
  4. Increased in system losses.
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