Sunday, 27 March 2016

Measurement of Medium Resistance by Substitution Method

In Substitution Method, the Resistance whose value is to be measured is compared with the Standard Resistance by some technique which is described in this section. The connection diagram for Substitution Method is given below.

Here, R is the unknown Resistance, S the Standard variable Resistance, A is Ammeter and r is Regulating Resistance.

When we put the Switch at position 1 then R is connected in the circuit. The Regulating Resistance r is adjusted till the reading of Ammeter is at a chosen scale mark. Now the Switch is thrown to position 2 putting the Standard variable Resistance S in the circuit. Now the variable Resistor S is adjusted till the reading of Ammeter is same as when R was in the circuit. The setting of dial of S is read. Since the substitution of one resistance for another has left current unaltered, and provided that EMF of battery and position of Regulating Resistance r remain unaltered, the two Resistance R and S must be equal. Thus the value of unknown Resistance R is equal to the dial setting of Standard Resistance S.

This method of measurement is more accurate as compared to the Ammeter Voltmeter Method as in this method measurement is not affected by the accuracy of Ammeter. However, the accuracy of this method is greatly affected if there is any change in the Battery EMF during the time when the reading in two settings is taken. Therefore to avoid the error because of change of EMF of Battery, a Battery of enough capacity is used so that it remains constant during the entire period of testing.

The accuracy of this method also depend on resistance of circuit excluding R and S, upon the sensitivity of instrument and upon the accuracy with which the Standard Resistance S is known.

This method is not widely used for simple Resistance measurement and is used in modified form for the measurement of High Resistance. The Substitution Method is however very important as it finds its use in application of bridge method and in high accuracy A.C measurement.

Example: In measurement of Resistance by Substitution Method, a standard 0.5 MOhm resistor is used. The Galvanometer has a resistance of 10 KOhm and gives raeding as follows:
  • With Standard Resistor, 41 division
  • With unknown resistor, 51 division.
What will be the value of unknown resistance?

Solution:  As the deflection of Galvanometer is directly proportional to the current flowing through the circuit which in turn depends on the net resistance in the circuit. Current through the circuit is inversely proportional to the net resistance. Let say a1 is the deflection of Galvanometer when standard Resistor S is in circuit and a2 when unknown Resistance R is in circuit.

So, a1/a2 = (R+G)/(S+G) where G is Galvanometer resistance.

So, 41/51= (R+G)/(S+G)

R = (S+G)×41/51 = 0.4×106 Ohm = 0.4 MOhm

Saturday, 26 March 2016

Voltmeter Ammeter Method for Measurement of Resistance

Resistance is classified into three categories for the sake of Measurement. Different categories of Resistance are measured by different technique. That’s why they are classified. They are classified as

Low Resistance:  Resistance having value 1Ω or below are kept under this category.

Medium Resistance: This category includes Resistance from 1Ω to 0.1 MΩ.

High Resistance: Resistance of the order of 0.1 MΩ and above is classified as High resistance.

In this section, we will discuss the method of measurement of Medium Resistance. The different methods used for Medium resistance are as follows:
·         Ammeter Voltmeter method
·         Substitution Method
·         Wheatstone Bridge Method
·         Ohmmeter Method

Ammeter Voltmeter Method:

There are two possible connections for the measurement of Medium Resistance using Ammeter Voltmeter Method as shown in figure below:
In both the cases, the reading of Voltmeter and Ammeter is taken. If the Voltmeter reading is V and Ammeter reading is I then the measured Resistance will be
Rm = V/I

Saturday, 19 March 2016


It is impossible to make a perfect / ideal circuit component which can have only one property. For example a Resistor do not have only resistance rather it have associated inductance and Capacitance too. Same is the case with Capacitor and Inductor. Therefore a circuit component have some impurity which causes unwanted quantities in the circuit known as Residues. However, a particular quantity such as resistance in a Resistor, capacitance in a capacitor and inductance in an Inductor are made to dominate to negligible effect of residue.

Resistor: A resistor is a device which offer resistance. The design of resistor is such that it satisfies the following properties:
  • Stability with time
  • Low temperature coefficient of restivity
  • Low thermo electric emf with Copper
  • High Resistivity
  • Resistant to oxidation, corrosion and moisture.
As no single material can have all these properties therefore selection of material is done based on the application of Resistor. Material used for Resistor are describe in below section.

  • Manganin: Manganin is an alloy of Copper, Manganese and Nickel. It has nominal composition of 84% Copper, 12% Manganese and 4% Nickel.It has high resistivity nearly 25 times that of the copper. When properly heated it gives stability with aging.The most important of Manganin is that it has zero temerature coefficient of resistivity at room temperature. Therefore it is most suited for making precision resistor for applications where temperature rise is not expected above 15 to 20 degree celcius.
  • Constantan: It is an alloy of Nickel and Copper containing 40 to 60% Nickel with small amount of Manganese to improve the mechanical properties. It is sold as Constantan or various other trade name for thermo electric material. It has thermo electric emf against copper of about 40  µV/°C. Except for their high thermo electric emf, their electrical property is similar to that of Manganin. It has resistivity of about 25 times that of Copper, it corrosion resistant and inexpensive. It can easily be soldered with copper. Therefore it finds a great application where thermo electric emf with copper is not disadvantageous. It is used for making resistor 1000 Ω and above for use in Voltmeter Multiplier.
  • Nickel Chromium Alloy: This alloy has higher temperature coefficient of resistivity than Manganin and Constantan. This alloy is not used for making precision resistor rather used for making rough class of resistor where small size of resistor is required. Nichrome has resistivity of about 50 times that of Copper.The most important property of this alloy is that it remain stable and corrosin resistant even at higher temperature.
  • Gold Chromium: It is an alloy of Gold and Chromium having 2% chromium. This alloy has resistivity about 20 times that of Copper. The temperature coefficient of this alloy can be made very small by baking it at fairly low temerature. It has thermo electric emf of 7 to 8 µV/°C with Copper.
Spools / Frames for Resistance Coil: Metallic spools are used for high quality d.c resistors instead of wooden spools because  of following advantages:
  • Metallic spool do not absorb moisture from surrounding like wooden spool. Therefore, they do not either expand or contract because of change of humidity. Hence, no stress is produced in the resistance coil and hence no change in resistance value.
  • Metal spools dissipates the heat energy produced in the Resistance because of flow of current. As the Resistance coil is in intimate contact with the spool, therefore heat produced in the resistance is transferred to the spool. This heat energy is then transferred from spool to the surrounding by convection and radiation. Thus an effective cooling is achieved by metallic spool.
  • Metal spools are normally made of Brass as the coefficient of thermal expansion of Brass is almost equal to that of Resistance coil. Because of which no differential thermal expansion is produced and hence no stress is developed.
  • For A.C application, metallic spools are not desirable because of Eddy Current Loss. Ceramic is universally used material for spool for A.C resistor. The disadvantage of Ceramic spool for precision resistor is that it have poor thermal conductivity as well as poor coefficient of linear expansion as compared to the Resistance wire. This leads to the differential expansion which causes stress with change in temperature.  
Resistance Wire:The Resistance wire is generally double silk or silk and cotton covered.The wire is enameled before these coatings are applied. High quality resistors are wound with only one layer of wire. The advantage of this are: 

  • Heat dissipation is more efficient.
  • Single layer coil are more stable.Multi layer coil are very pron to change their resistance because of change of atmospheric humidity.
  • Multi layer resistance are found to be less stable for its resistance value with aging.
Low Resistance Standard: Low Resistance has value less than 1 ohm. Low resistance standard are Four Terminal Type. They are provided with two current terminals C and C' & two potential terminals P and P' as shown in figure. While in two terminal resistor only two current terminals C and C' are provided.

In two terminal resistor, the resistance measured between the two terminals C and C' = V/I which also include the Contact Resistance of the Connecting Leads to terminals C and C'. The value of contact resistance is normally 0.001 ohm so if the value of resistor is 1 ohm then measured resistance in two terminal resistor = 1+0.001 = 1.001. Therefore the percentage error in the measurement = (0.001/1)*100 = 1%.

Now suppose the value of standard resistance is 0.1 ohm the percentage error will be (0.001 / 0.1)*100 = 10%. Therefore error is increasing because of Contact resistance of connecting leads as we are measuring the low resistance. 

In Four Terminal Resistor, Voltage = Between the potential terminals P and P' which are located in the middle portion of the Resistor.

The value of Resistance between the potential terminals P and P' is called nominal Resistance. As P and P' are located in the middle portion of the Resistor hence effect of Contact resistance of the connecting lead is ruled out. Also the current distribution in the middle part of Resistor is uniform therefore it gives a correct value of resistance.

This principle is used in the measurement of contact resistance in the joints between Circuit Breaker and conducting Bus bar, Current Transformer and connection bus etc. If you want to get detail of Measurement of Contact Resistance Measurement by four terminal method, follow me.

Effect of Frequency on Resistor: A Resistor may be represented by an equivalent circuit as shown below.

This equivalent circuit is valid for low and Medium frequencies. This circuit shows and Inductance L in series with D.C Resistance R and the combination shunted by Capacitance C. Let Z be the equivalent impedance at angular frequency ω rad/sec.  

So, Z = (1/jωC)(R+jωL) / {R+jωL+(1/jωC)}
         = [R+jω(L-ω2L2C-CR2)] / (1+ω2C2R2-2ω2LC+ω4L2C2)

For a Resistor, L and C are very small, hence ω4L2C2~0

Z = [R+jω{L(1-ω2LC)-CR2} / [1+ω2C(CR2-2L)]

Writing the Real and Imaginary parts, we get

Effective Resistance Reff = R/ [1+ω2C(CR2-2L)]

Effective Reactance Xeff = ω{L(1-ω2LC)-CR2} / [1+ω2C(CR2-2L)]

As Xeff is very small, therefore ω2LC may be dropped.

Xeff = ω{L-CR2} / [1+ω2C(CR2 _ 2L)]

Therefore, the effective Inductance,

So, Leff = {L-CR2} / [1+ω2C(CR- 2L)]

The effective Inductance is also called Residual Inductance. The effect of Residual Inductance in a Resistor may be expressed by Phase Defect Angle Ø by which current lags the applied voltage.

tanØ =  Xeff / Reff
         = ω (L/R-CR)

The characteristics of Resistor is also expressed in terms of Time Constant Ƭ,

Ƭ = Leff / Reff
   = L/R – CR

Therefore, it is clear that time constant of resistor may either be positive or negative depending upon whether L/R is greater than CR or not. If L/R is greater than CR then Ƭ is positive. This is the case for small resistor (1 to 10 ohm) in which Inductance dominates over Capacitance. For higher value of resistance (above 1000 ohm) capacitance predominates over Inductance and hence Ƭ is negative for Higher Value Resistor. The time constant of a Resistor is an indicator of its performance at higher frequencies and its value ranges from 0.5 to 1 micro seconds.

For D.C Resistance to be equal to effective Resistance Reff, R = Reff

So, CR2 = 2L…………..For R = Reff

If Resistance to show no inductive effect then Xeff = 0

Which means L = CR2

For Resistor, Inductance should be as low as possible, therefore L = CR2 and hence in that case D.C value of resistance will be equal to A.C value. Effective Resistance for zero Inductance will then be

Reff = R / [1- ω2LC]

Also,as R2 = L/C, hence for small Resistor, it should be designed so that Inductance is very low and Capacitance is high.

Wednesday, 16 March 2016

Measurement of Capacitance and Dissipation Factor

We will discuss how to measure Capacitance and Dissipation Factor. Capacitance is measured by using Schering Bridge. What is this Schering Bridge? First we will discuss how to balance a bridge.

As we know for balanced bridge,

Tuesday, 15 March 2016

Capacitance and Dissipation Factor

A Capacitor is a device which has the capability to store energy in its Electric Field. Therefore we can say that a Capacitor can store charge. There are many types of Capacitor but the most basic Capacitor is Parallel Plate Capacitor. We will consider this basic capacitor for getting idea of basic but important parameters of Capacitor.
A parallel plate Capacitor is made of two plates separated by some distance. Let’s assume that the separation between the plates is d. We apply a DC voltage across the parallel plate. What will happen then?
Obviously the charges will start to accumulate on the plate and will continue to accumulate until the potential difference between the plates becomes equal to applied Voltage V. Say charge +Q is accumulated on one plate and –Q on another plate. Then mathematically we can have
Q = CV

Here the term C is known as Capacitance.

Does the Capacitance depend upon the Voltage applied across the Capacitor?

You might answer yes. But it’s not correct. Capacitance only depends upon the physical dimension, dielectric and geometry of Capacitor. In fact the value of Capacitance for a parallel plate Capacitor is given as

C = E0ErA / d

Where E0 = Permittivity of free space.
            Er = Relative permittivity of dielectric.
            d = Separation between the plates.
            A = Cross sectional area of plate
So, from the above it is quite clear that Capacitance depend only on dimension, dielectric and geometry.

A Capacitor finds much use in Electrical Engineering and Technology. The size of Capacitor varies from very small to large one. The application of Capacitor ranges from tiny electronic circuit to 765 kV Circuit Breaker as Grading Capacitor. Therefore, it is very much important Capacitor is in pure state but honestly speaking it is much difficult to manufacture pure Capacitor rather it have some resistance in it which causes ohmic loss. Therefore, the measurement of this loss is much needed. The question arises how do we measure this loss? The answer is simple, by measuring Dissipation Factor. 

What is Dissipation Factor?
For answering this question we need to realize a real Capacitor. A Capacitor can be realized as series combination of small resistance of dielectric medium and capacitance as shown in picture below.

If we draw the phasor diagram, it will look like,

If the Capacitor had been pure then it would have taken current Ic leading by angle 90 degree but because of resistive component of dielectric, net current drawn is deviating from 90 degree by some angle δ. This angle δ is hence called Loss Angle. From the phasor diagram, it is clear that

tanδ = Ir / Ic = Capacitive leakage current / Resistive leakage current.

This tanδ is also called Dissipation Factor. Why called Dissipation Factor? Be patient, you will come to know latter in this topic.

Now, we will calculate the Power Factor of the Capacitor. If the Capacitor would have been pure then the P.F would have been Cos90 = 0 but because of some resistive component it will no more be zero rather it will be something close to zero like 0.001.
CosØ = Cos(90-δ) = Sinδ

As is angle δ is very small, hence Sinδ ~ tanδ~δ
Therefore, dielectric loss = VICosØ = VISinδ
                                            = VIcSinδ/Cosδ
                                            = VIctanδ
Therefore, dielectric loss is proportional to tanδ. That is why tanδ is often called Dissipation Factor too. For a good capacitor, obviously the value of tanδ should be very less as it will cause less dielectric loss.


In my next post, you will learn how do we measure Capacitance and Dissipation Factor. Be patient till then and follow me. Thank you

Sunday, 13 March 2016

Dynamic Contact Resistance Measurement, DCRM

First question which strikes in our mind is that why do we need to do DCRM even though we already had Contact Resistance Measurement,CRM? Seems good question and this question will take you to the depth.
So, first of all we need to know about the contacts of Circuit Breaker. Basically, a CB has two types of Contact.
  • Main Contact– Main contact of CB are designed to carry current when the CB is closed but it is not designed to take arcing stress during Closing / Opening operation of CB. Therefore, obviously Main Contact will make after the making of Arcing contact during Closing operation and it will separate before the separation of Arcing contact during Opening operation.
  • Arcing Contact– Arcing contact is provided in CB to take all the arcing stress.
BreakerFrom the picture, it is clear that how arcing contact and Main Contact work. When we measure the CRM, we do it after closing the CB so the measured resistance is basically the Net Resistance of Main Contact and Arcing Contact. If the Resistance of Main Contact is R and that of arcing contact is r the both of them are parallel when Breaker is closed. So measured resistance during CRM = R*r/(R+r)
Next, If I ask you how will you determine whether the Arcing Contact assembly is properly working or malfunctioning then will you answer by doing CRM? Obviously your answer will be a big NOOO………..
How will we confirm then? It’s by conducting DCRM.
Why dynamic? As because the arcing contact travels while Opening / Closing operation to fully take closed position / open position. Therefore the word Dynamic came in picture. Therefore as you can guess, DCRM measures the contact Resistance during dynamic condition. Basically it is the measurement of Arcing contact resistance when contact travels.
How do we conduct this test and what are the results?
This test is conducted by DCRM kits available in market of many makes like SCOPE, DOBLE etc. What we do, we extend the 220 V DC supply to the kit and form the kit 220 V DC is extended to the nearest point of Trip Coil-1 & TC-2 and Closing Coil. By this manner we take the control to kit for closing / opening of Breaker. For taking the Breaker Open / Close feedback to the kit, we connect the kit to the NO contact of Auxiliary Switch of CB. Now, we need to get the travel of contacts, for that we connect kit to the closing / opening lever via a Transducer. By this manner, we are now able to control the CB, Status of CB and contact travel in kit.
DCRM kit now injects 100 A / 25 A current through the contacts and plot a curve of Current through the contact during dynamic condition, Travel of contact and Dynamic Resistance with respect to Time. Straight forward, a fingerprint of CB we get.
How does the fingerprint looks and how to interpret?
This a typical fingerprint of healthy CB. How do we analyse this signature of CB?
See the graph, there are three quantities namely Resistance (Dynamic), Current and Travel of Contact. Lets start when the CB is open, obviously Resistance will be high as shown by horizontal red line. But as soon as we give close command to the CB, first Main Contact makes and resistance decreases to point P1. After that Arcing Contact start closing, resistance varies from P1 to P2 and finally when it is fully closed the resistance is constant P2 to P3. At P3, CB is fully close. Now we will see what happens to the Current.
Initially current is zero as CB is open. As soon as we give close command to the CB,at P1 current increases and at P2 it will be highest as CB is fully close here. Current will remain at its maximum up to P3.
At P3 we give opening command to the CB by the Kit, so Main Contact will open at P3 and Resistance will increase slightly to P4, and then Arcing Contact start opening and at P4 it fully opens and hence Resistance take the maximum value. Likewise current also, decreases to its original value i.e zero.
Now we focus on Travel of contact. Leaving this portion for you to think but in case you need help write in comment box.
Now, see the dynamic period is from P2 to P3 as in this period Arcing contact is travelling to get at fully close position. Therefore, during the dynamic period the Resistance curve is almost flat which signifies constant resistance during dynamic period which in turn meand Arching contact and main contact assembly are properly working and contacts are in good condition. Now take a look at this Signature of CB.
Bad CB
See the dynamic resistance(Green curve) during Close / Open period is not flat rather it is fluctuating which means contact condition is not good or assembly is malfunctioning.
That is all which I can convey. If you have more information share it by writing in comment box, I will be very happy. Thank you!!!

DC Shunt Motor Charatersitics

Long Shunt and Short Shunt DC Compound Machine:
In short shunt DC Compound Machine, shunt filed winding is connected across the Armature whereas in Long shunt connection it is connected across the line terminal. But there is no difference in operating characteristic in two types of machine.
Characteristics of DC Shunt Generator:
There are four basic quantities related to generator namely speed n, Terminal Voltage Vt , Armature Current Ia and Field Current If

The graphical relationship between two quantities while maintaining other two quantities constant is known as characteristics of Generator. Basically, there are four characteristics of any Generator:
1.    No load Characteristics:- Relationship between Ea and If. Ea = f(If)
2.    Load Characteristics:- Relationship between Vt and If. Vt = f(If)
3.    External Characteristics:- Relationship between Vt and IL. Vt = f(IL)

4.    Armature / Regulation Characteristics:- Relationship between If and Ia. If = f(Ia)
1.    No load and Load Characteristics:
2.    External Characteristics:
3. Armature Characteristics:

DC Motor Starter

D. C Motor Starting:

Why Starter Needed:

Let Vt  = Terminal Voltage
Ia = Armature Current
ra = Armature Resistance
Ea = Back emf = KaØWm

At the time of starting, speed of motor is zero hence Wm = 0, therefore there will not be any Back / Counter emf. Hence if we look into the equation,

Vt= Ea+ Iara
   = 0+ Iara
Hence Ia = Vt / ra

Since the value of armature resistance is very less of the order of 0.1 to 0.5 hence if rated voltage is applied to the Motor then motor will draw excessive current from the Supply mains. Such heavy inrush current may result into
1.    Sparking at commutator.
2.    Damage to armature winding and damage of insulation over it due to overheating.
3.    Large dip in supply voltage.
4.    High starting torque and quick acceleration which may result in damage of rotating part of the motor.

General Philosophy of Starter:
The primary function of a Starter should therefore be to limit the starting current and acceleration time of motor. Therefore if we insert a resistance in series with the armature circuit, it will limit the starting current but as the motor accelerates back emf will be developed which in turn will reduce the armature current, therefore as the motor accelerates the inserted resistance must be decreased.

While starting the DC Shunt Motor / DC Compound Motor, field flux should be kept maximum as the result in low operating speed which means less acceleration time. Also as Torque = KaØIa, hence starting torque needed to overcome the frictional force will be met by less armature current. So rheostat in series with field circuit should be kept at zero position while starting the machine.
DC Shut / Compound DC Motor Starter: Mind that staring resistor is inserted in armature circuit not in field circuit.
There are two types of starters for Shunt and Compound DC Motor:
  1.  Three point starter
  2. Four point starter

For DC Series Motor No load Release type starter is used. Mind that staring resistor is inserted in armature circuit not in field circuit.

Wanna know detail of these starters? Just write in comment box, it will encourage me friends