Category Archive Basics of Electrical Engineering


Effect of Electric Shock Currents on Humans

The human body experiences shock due to flow of current through the body and not due to the voltage level. If the human body is properly insulated he or she can even hold bare high voltage wire. It is a usual sight to see birds sitting on the wire of HT lines. However, if the birds span the two HT wire simultaneously, it will turn into a dead short circuit.

In general, shock currents are classified based on severity of the shock they cause according to this these are divided into two types:

Primary Shock Currents

The currents which produce direct physiological harm are termed primary shock currents.

Secondary Shock Currents

The currents which do not cause direct physiological but may cause involuntary muscular reactions are called secondary shock currents.

It is to be noted that the threshold value of current which gives a tingling sensation on the hand or finger when touching an electrically live device differs from person to person. For a normal healthy person a current of 1 mA is the threshold value to produce tingling sensation. Currents of about 10 to 30 mA can cause lack of muscular control.

A human heart can be considered as a muscle operating rhythmically due to a nerve pulse that provides the heart beat. Therefore, when an external signal due to electric current is sent into the heart which will have different frequency, different from that of the normal heart, it disturbs the rhythmic flow of operation of heart. This condition of operation is known as ventricular fibrillation or arrhythmic operation of heart. Once this arrhythmic condition is set up, it is difficult to stop. It usually requires injection of another electric current to stop the fibrillation and reestablish the normal rhythm.

Typical effects of Electric shock currents on humans

50 Hz Current


0-1 mA

No sensation

0-3 mA

Mild sensation

3-5 mA

Pain or annoyance

5-10 mA

Painful shock

10-15 mA

Local muscle contraction

30-50 mA

Breathing difficult, can cause unconsciousness

50-100 mA

Possible ventricular fibrillation of heart

100-200 mA

Ventricular fibrillation of heart certain.

It is to be noted that the effect of electric shock currents not only depends upon the physiological features of a person but the psychologic factors also play an important part. The effects of electric current on vital human organs not only depend upon the magnitude of currents but it depends upon the duration and frequency of the current. Humans are more vulnerable to electric shock current at 50-60 Hz. The human body can withstand slightly higher current at 25 Hz and almost five times larger for d.c. current. Similarly at frequencies of 1 KHz or 10 KHz even larger currents can be tolerated. In case of lightning (where the frequency is very high and duration is in µ secs) the human body can withstand very high currents in terms of several hundreds of amperes.


Difference Between Resistor, Rheostat and Potential Divider


A fixed resistance connected permanently in the circuit for limiting the current to a definite value is known as a resistor. It should be capable of withstanding the temperature developed in it.


A variable resistance by sliding contact on it is called a rheostat. The current flowing through the circuit is controlled by inserting and varying the with the help of sliding contact.

Potential Divider

When a resistance is used to develop a voltage drop, it is called a potential divider.


Lenz’s Law

The direction of the induced current may also be found by this law which was formulated by Heinrich Lenz in 1835. Heinrich Lenz was a Russian geologist and Physicist. Hence, the name of this law is Lenz’s Law.

Statement of Lenz’s Law

This law states, in effect, that electromagnetically induced current always flows in such direction that the action of the magnetic field set up by it tends to oppose the very cause which produces it.


The above statement will be clarified from the following explanation.

Lenzs LawIt is found that when N-pole of the bar magnet approaches the coil, the induced current set up by induced e.m.f. flows in the anticlockwise direction in the coil as seen from the magnet side. The result is that face of the coil becomes a N-pole and so tends to oppose the onward approach of the N-Pole of the magnet (like poles repel each other). The mechanical energy spent in overcoming this repulsive force is converted into electrical energy which appears in the coil.

When the magnet is moved away from the coil, the induced current flows in the clockwise direction thus making the face of the coil (facing the magnet) a S-pole. Therefore, the N-pole of the magnet has to withdrawn against this attractive force of the S-pole of coil. Again, the mechanical energy required to overcome this force of attraction is converted into electric energy.

It can be shown that Lenz’s law is a direct consequence of Law of Conservation of Energy. Imagine for a moment that when N-pole of the magnet  approaches the coil, induced current flows in such a direction as to make the coil face a S-pole, Then, due to inherent attraction between unlike poles, the magnet would be automatically pulled towards the coil without the expenditure of any mechanical energy. It means that we would be able to create electric energy out of nothing, which is denied by the inviolable Law of Conservation of Energy. In fact, to maintain the sanctity of this law, it is imperative for the induced current to How in such a direction that the magnetic effect produced by it tends to oppose the very cause which produces it. In the present case, it is relative motion of the magnet with magnet with respect to the coil which is the cause of the production of the induced current. Hence, the induced current always flows in such a direction to oppose this relative motion i.e., the approach or withdrawal of the magnet.


Eddy Current Loss

When a magnetic material is subjected to a changing magnetic field, an e.m.f. induced in the magnetic material itself according to Faraday’s laws of electromagnetic induction. Since the material is conducting, these induced voltages circulates currents within the body of the material. These circulating current is known as eddy currents.  As these currents are not used for doing  any useful work, therefore, these currents develop i2R loss in the material. This loss is known as eddy current loss. Like hysteresis loss, this loss also increases the temperature of the magnetic material. The hysteresis and eddy current losses in a magnetic material are called iron losses or core losses or magnetic losses.

eddy current loss

A magnetic core subjected to a changing flux shown in the figure. When changing flux links with the core itself, an e.m.f. is induced in the core which circulating currents in the core. These currents produce eddy current loss i2R, where i is the value of eddy currents and R is the resistance of the eddy current path. As the core is a continuous iron piece of large cross-section, the magnitude of i will be very large and hence greater eddy current loss will result.

The obvious method of reducing this loss is to reduce the magnitude of eddy current. This can be achieved by splitting the solid block into this sheets (called laminations) in the planes parallel to the magnetic field. Each lamination is insulated from the other by a layer of varnish. This arrangement reduces the area of each section and hence the induced e.m.f. it also increases the resistance of eddy current paths since the area through which the currents can pass is smaller.

The only drawback of laminated core is that the total cross-sectional area of the magnetic material is reduced by the total thickness of the insulation. This generally taken into account by allowing about 10% reduction in the thickness of core when making the magnetic calculations.

Applications of Eddy Currents

It has been seen that when the affects of eddy currents are not utilized, the power or energy consumed by these currents is known as eddy current loss. There some applications of eddy currents that are given below;

  • Induction heating
  • Eddy current damping torque.

Power Factor

The electrical energy is almost exclusively generated, transmitted and distributed in the form of alternating current. Most of loads are inductive in nature and have low lagging power factor. The low power factor is highly undesirable as it causes additional losses of active power in all the elements of power system from power station generator down to the utilization devices.

Current taken by any circuit consists of two components. One is the current transformed into the useful work is called working component Iw and the other is magnetizing current Iμ which often termed as wattless component because it does no useful work. Component Iw being in phase with the voltage and the component Iμ being in quadrature with the voltage represents no work and is mainly responsible for the creation of magnetism.power factorI2 = I2w+ I2μ

(KVA)2 = (KW)2 + (KVAR)2


The cosine of the angle between voltage and current is called is power factor.


It is the ratio of resistance to the impedance.


It is the ratio of true power to the apparent power.

Cause of Low Power Factor

  1. Most of the a.c. motors are of induction type which has low lagging power factor. These motors work at a power factor which is extremely small on light load and rises to 0.8 or 0.9 at full load.
  2. Arc lamps, electric discharge lamps and inductrial heating furnances operate at low lagging power factor.
  3. The load on the power system is varying ; being high during morning and evening and low at other times. During low load period, supply voltage is increased which increases the magnetization current. This results in the decreased in P.F.

Disadvantages of Low Power Factor

The magnitude of line current supplying a given balanced three phase load P at voltage V and P.F.  cosΦ is given as :

Low P.F. for a given load and supply voltage means more current. This has the following effects.

Large KVA rating of equipment

The electrical machinery (e.g. alternators, transformers, etc) always rated in KVA.

It is clear that KVA rating of an electrical machine is inversely proportional to power factor. The smaller the power factor, larger the KVA rating.  Therefore, at low P.F., the KVA rating of an electrical machine has to be made more, making an electrical machine larger and expensive.

Greater conductor size

For a given cross sectional area of line conductors, line losses are proportional to 1/cos2Φ. Poor power factor means more line losses and low transmission efficiency. Alternatively, if efficiency of transmission is to be kept same, poor P.F. will require cross-section of the line conductors which will be inversely proportional to 1/cosΦ. This will therefore increase capital investment in the transmission lines.

Larger copper losses

The large current at low P.F. causes more I2R losses in all the elements of the supply system. This result in poor efficiency.

Poor voltage regulation

Greater the value of phase angle difference or lower the value of P.F., greater will be the  value of voltage regulation. Extra voltage regulation equipment will be required to keep the voltage drop prescribed limits. Futher the armature reaction due to the lagging currents in an alternator being demagnetizing, it requires higher excitation to maintain given value of generated voltage, as P.F. of the load becomes poor. This will increase the rating of exciter too. This will again increase the cost.

Reduced handling capacity of system

The lagging P.F. reduces the handling capacity of all the elements of the system. It is because the reactive component of current prevents the full utilization of installed capacity.


Magnetic Circuit

Magnetic Circuit

The closed path followed by magnetic flux is known as magnetic circuit. A magnetic circuit usually consists of materials having high permeability.

The amount of magnetic coil depends upon current (I) and number of turns (N). If we increase the current or number of turns, the amount of magnetic flux also increases and vice versa. The product of NI is called magnetomotive force (mmf).

Analysis of Magnetic Circuit

l =  mean length of the magnetic circuit in meters

a =  effective area of the core in m2

μr  = relative permeability of the core material

N = number of turns

I = current passed through the circuit in ampere

Φ = flux set up in the core in weber

Important Terms of Magnetic Circuit

Flux:- The number of lines of force in a magnetic circuit is called flux. The unit of magnetic flux is the Weber (Wb). It is denoted by Φ.

Magnetomotive force:- It is a force that set up magnetic flux in a magnetic circuit. The unit magnetomotive force is AT.

mmf = NI ampere-turns (AT)

Reluctance:- The opposition that the magnetic circuit offers to magnetic flux is called reluctance. The unit of reluctance is AT/wb. It is denoted by S.

Reluctance depends upon the following factors:-

  • Reluctance of the magnetic circuit is directly proportional to the length of the magnetic path.
  • Reluctance of the magnetic circuit is inversely proportional to the effective area of the magnetic circuit.
  • The reluctance of the magnetic circuit is also inversely proportional to the relative permeability of the material.
  • Nature of material.

Permeance: – it is reciprocal of reluctance. The unit of permeance is Wb/AT.

Reluctivity: – It is the specific reluctance.

Analogy of Electric Circuits and Magnetic Circuits

Sr No.

Electric Circuit

Magnetic Circuit





Current (I)

Flux (Φ)


Resistance (R)

Reluctance (S)


Resistivity (Rho)

Reluctivity (1/μ)


Current Density (A/m)

Flux Density (Φ/m)


Dissimilarities of Electric Circuits and Magnetic Circuits

  • The resistivity of conductors is more or less constant but the permeability of the ferromagnetic materials varies greatly with magnetic field strength.
  • The flux does not actually flow in the sense in which an electric current flows.
  • In an electric circuit energy must be supplied, to maintain the flow of electric current in the circuit, whereas the magnetic flux once, it is set up, does not require any further supply of energy.

B-H Curve

The curve drawn between magnetic flux density (B) and magnetizing force (H) is called B-H curve.


Voltage and Current Sources

A voltage source is a source of   energy  which establishes a potential difference across its terminals. Most of the sources encountered in everyday life are voltage sources, e.g. batteries, d.c. generators, alternators, etc. The current source is a source of energy that provides a current e.g., collector circuits of transistors. Voltage and current sources are called active elements because they provide electrical energy to a circuit.

Ideal voltage Source

An ideal voltage source is one which maintains a constant terminal voltage, no matter how much current is drawn from it. An ideal voltage source has zero internal resistance.

Practical Voltage Source

A practical voltage source has very low internal resistance, that causes its terminal voltage to decrease when load current is increased and vice-versa.

Ideal Current Source

An ideal current source is one which maintains will supply the same current to any resistance connected across its terminals. An ideal current source has infinite internal resistance.

Practical Current Source

A practical current source has very high internal resistance. Therefore, the load current will change as the value of load resistance changes.


Fleming’s left and Right Hand Rule

Fleming’s Left Hand Rule

Fleming’s Left-hand Rule. Stretch out the First finger, second finger and thumb of your left hand so that they are at right angles to one another. If the first finger points in the direction of the magnetic field  and second finger points towards the direction of current, then the thumb will point in the direction of motion of the conductor.

flemings left hand rule

Pic Courtesy Wikipedia

Fleming’s Right Hand Rule

Stretch out the forefinger, middle finger and thumb of your right hand so that they are at right angles to one another. If the forefinger points in the direction of the magnetic field, thumb in the direction of motion of the conductor, then the middle finger will point in the direction of induced current.

This law is particularly suitable to find the direction of the induced e.m.f. and hence current when the conductor moves at right angles to a stationary magnetic field.


Types of Resistors

A component whose function in a circuit is to provide a specified value of resistance is called a resistor. The resistors are used to limit the circuit current, divide voltage and in certain cases, generate heat.  Although there are a variety of different types of resistors, the following are the commonly used resistors in electrical and electronic circuits:-

  • Carbon composition types
  • Film resistors
  • Wire-wound resistors
  • Cermet resistors

Carbon Composition Type

This type of resistor is made with a mixture of finely ground carbon insulating filler and a resin   binder. The ratio of carbon and insulating filler decides the resistance value. The mixture is formed into a rod and lead connections are made.  The entire resistor is then enclosed in a plastic case to prevent the entry of moisture and other harmful elements from atmosphere.

carbon composition resistors

Carbon resistors are relatively inexpensive to build.  However, they are highly sensitive to temperature variations. The carbon resistors are available in power ratings ranging from 1/8 to 2 W.

Film resistors

In a film resistor, a resistive material is deposited uniformly onto a high grade ceramic rod. The resistive film may be carbon (carbon film        resistor) or nickel-chromium (metal film resistor). In these types of resistors, the desired resistance  value is obtained by removing a part of the resistive material in a helical pattern along the rod.

Wire-Wound Resistors

A wire wound resistor is constructed by winding a resistive wire of some alloy around an insulating rod.  It is then enclosed in an insulating cover. Generally, nickel chromium alloy is used because of its very small temperature coefficient of resistance.

wire wound resistors

Wire-wound resistors can safely operate at higher temperatures than carbon types. These resistors have high power ratings ranging from 12 to 225 W.

Cermet resistors

A cermet resistor is made by depositing  a thin film of metal such as nichrome or chromium cobalt on a ceramic substrate.  They are cermet which is a contraction for ceramic and metal.  These resistors have very accurate values.

cermet resistors


Faraday’s Laws of Electromagnetic Induction

Electromagnetic Induction

The phenomenon of production of e.m.f. and hence current in a conductor or coil when the magnetic flux linking the conductor or coil changes is called electromagnetic induction.

There are two laws of electromagnetic induction, that are explained below:-

Faraday’s First Law of Electromagnetic Induction

This law states that, when the magnetic flux linking a conductor or coil changes, an e.m.f. is induced in it. It does not matter how the change in magnetic flux is brought about. The summary of the first law of electromagnetic is that the induced e.m.f. develop in a circuit subjected to a changing magnetic field.

Faraday’s Second Law of Electromagnetic Induction

The magnitude of the e.m.f. induced in a conductor or coil is directly proportional to the rate of change of flux linkage.