Linear Variable Differential Transformer

Linear Variable Differential Transformer or LVDT is a displacement transducer, which is mainly used for measurement of linear displacements. LVDT works on the principle of transformer action i.e., mutual induction between primary and secondary coils. 

Construction of LVDT

LVDT essentially consists of a transformer which has one primary coil and two secondary coils with a movable core. Secondary coils are placed symmetrically relative to primary coil. Both secondary coils have equal number of turns and they are identical with each other. Secondary coils are connected in series opposition and when transformer is energized the two voltages induced in two coils have phase difference of 180⁰. Core is placed in between primary and secondary coils and allowed for free movement along its axis as shown in figure given. Core is made up of magnetic material and it facilitates magnetic flux linkage between primary coil and secondary coils. The objects or shafts whose displacements are to be measured are coupled with one of the ends of core. 

Working Principle of LVDT

Like a transformer, LVDT also works on the principle of mutual induction between primary and secondary coils as it's construction is just similar to a transformer but instead of two coils (one primary and one secondary) LVDT's transformer has three coils (one primary coil and two secondary coils). Further, two secondary coils are connected in series opposition in such a way that when transformer is energized the two voltages induced in two coils have phase difference of 180⁰ or simply we can say that two voltages induced in two secondary coils have reversed polarities so that addition of emfs induced in both coils because of linear displacements of core becomes net output of LVDT. When core moves up or down from central position about its axis, LVDT gives some output because magnetic flux linking each secondary coil changes and are not same which in turn produces voltages of different magnitudes and of reversed polarities in coils.

Working of LVDT

The object whose displacement need to be measured is attached to the core by suitable means. With the displacements of objects, core is moved either up or down. When core is moved towards down-side from central position, magnetic flux linking with secondary coil 2 (SC2) increases whereas magnetic flux linking with secondary coil 1 (SC1) decreases. Thus, the voltage induced in SC2 increases and in SC1 decreases. As discussed above, voltage induced in SC1 & SC2 are 180⁰ out of phase that is these voltages have reversed polarities than each other. Also these secondary coils are connected in series, therefore, addition of voltages in two coils is the net output voltage of LVDT. For example, say at any instance voltage induced in coils SC1 is -2 volts and in coil SC2 is 5 volts, so net output voltage will be 3 volts. This voltage will have same phase as SC2. Similarly, when core is moved up-side from central position, voltage induced in SC1 increases and in SC2 decreases. Thus net output will be the addition of two voltages. On the other hand, when core is at central position, magnetic flux linking with SC1 & SC2 are same and voltages induced in both coils are also same but with polarities reversed than each other. Thus, net output voltage of LVDT will be zero.


Because of residual voltages due to stay magnetic and capacitance effects, the net output voltage at central position may not zero at all the times. LVDTs are available in wide ranges. LVDTs have linear output over a wide range of input displacements.

Advantages of LVDT Instruments

• Minimum input force costs in sensing by LVDT because of negligible friction in movement of force.
• High sensitivity.
• Linear Output.

Resistors, Resistivity, Color Coding of Resistors

     Resistor is an electronic or electrical component that opposes the flow of current in a circuit. Such an oppose by resistors to flow of current is known as resistance. Practically all materials offer some resistance to flow of current.

     Resistors are most common components used in electronic circuits. Usually resistors have two leads which are connected in series with other components in the circuit to limit flow of current through components connected in circuit.

     Resistance of a Resistor is measured in "Ohm". The symbol used to represent Ohm is a Greek letter "Ω" (Omega). Symbol used to represent the Resistor is "R" and figure representation of Resistor is given below ;

Symbol of Resistor

Another way of representation symbol of Resistor

RESISTIVITY 

     Resistivity or Specific Resistance of a substance is defined as the resistance of a unit long wire having a unit cross-section area, which is kept at 20⁰ C. Symbol used to represent the resistivity is a Greek letter "ρ" (Rho). SI unit of measurement of Electrical Resistivity or Specific Resistance of a substance is "Ω-m".

IMPORTANT ; As the resistance of a substance is a function of size, shape and environmental conditions of the substance, thus Resistivity becomes a very important term because it gives a means of comparing resistance of various substances and help us determining best conductors among others.

RELATIONSHIP BETWEEN ELECTRICAL RESISTANCE AND ELECTRICAL RESISTIVITY OF A SUBSTANCE 

Let us assume a piece of substance having ;

1. Resistance = R  Ω
2. Resistivity = ρ  Ω-meters,
3. Length = L meters, &
4. Cross-sectional Area = A square meters

 {because resistance is proportional to length and

   inversely proportional to cross-sectional area}

FACTORS DETERMINING RESISTANCE 

     From the equation between electrical resistance & electrical resistivity of a substance explained above, now we can say that the factors determining resistance are resistivity (ρ), shape i.e. length & cross-sectional area. Also, environmental conditions i.e., temperature affects resistance. All these factors have been explained below ;

Resistivity ( ρ ) ;
     We know that resistivity or specific resistance of a substance is the resistance of a unit long wire having a unit cross-sectional area at 20⁰ C and resistivity is proportional to resistance. So higher the resistivity will be, the higher will be the resistance of that substance and vice versa.


Length ;
     Length is also proportional to the resistance. Therefore, a wire with a longer length say 15 meters will have higher resistance to electric current flow than a wire of not so long length say 10 meters, if other conditions like resistivity, cross-sectional area and temperature are kept unchanged. This is because the resistive path increases with the length.


Cross-sectional Area ;
     Cross-sectional Area is inversely proportional to the resistance. Therefore, a wire with a bigger cross-sectional area will have less resistance than a wire having comparatively smaller cross-sectional area, if other conditions like resistivity, length & temperature are kept unchanged. As we know that current is the flow of electrons through a conductor when we apply electro-motive force or voltage across a conductor. This means, number of loosely bounded electrons will be more if cross-sectional area is increased and conductor allows current flow with ease and thus resistance experienced by flow of current will also decrease.


Temperature ;
     Different materials have different properties and also change in temperature affects their resistivity differently. Resistance of some substances increase with increase in temperature and vice versa. Such substances are said to have positive temperature coefficient. Resistance of some other substances decrease with increase in temperature and vice versa. Such substances are said to have negative temperature coefficient.

CLASSIFICATION OF RESISTORS   

Classification based on applications ;

• Fixed Value Resistors 
• Variable Resistors

Classification based on constructional features ;

• Carbon composite filled resistors
• Wire-wound resistors
• Deposited film resistors

Classification based on input signal sensing principle

• Light Dependent Resistors (LDRs)
• Thermistors

All these resistors classified above have been explained below ;

CARBON COMPOSITE FILLED RESISTORS 

     These are fixed value resistors and most commonly used resistors. In these resistors, resistive path or resistance to current flow is obtained with the help of mixture of composite materials including fine carbon particles which are conductive in nature and fine particles of other suitable non-conductive materials which are used to bind mixture and hold them tightly together. This tightly bounded carbon composite looks like a cylindrical in shape which is protected inside ceramic coating and two connecting metallic leads, one at each end are joined to make connections in circuits.

     Desired resistance value is obtained by increasing or decreasing carbon contents in the mixture.

WIRE-WOUND RESISTORS 

     These resistors essentially consists of a length of wire of specific resistance (alloy of various suitable metals), which is wrapped around a core of non-conductive materials usually ceramic core. Wire is wrapped around in such a way that it runs from one end to another so that two connecting leads are obtained from core ends i.e., one connecting lead is available at each end. Also resistive wire is wrapped spirally around core in such a way that it does not make contact radially at any point throughout its length. Wire wound resistors are especially used where high wattage resistors are required. These resistors are available in various shapes and sizes. Wire-wound resistors are also made available as fixed value resistors as well as variable resistors. Examples of variable wire-wound resistors are Rheostats & Wire-wound potentiometers.

     Desired resistance value is obtained by selecting alloy metal for resistive wire to make resistive path and also by increasing or decreasing length of wire. Alloy metals used for wire and its cross-sectional area also determine wattage rating of resistors.

DEPOSITED FILM RESISTORS  

     These resistors, as name suggests, are made by depositing layer of resistive material, which may contain carbon film of metallic film, onto a core of some non-conductive material. Rest of its construction is similar to that carbon composite filled resistors.

RHEOSTATS RESISTORS 

     These are wire-wound type of resistors. These are variable resistors. Rheostats are analog devices. Various resistance values are obtained by a slider. A slider is a simple sliding mechanism which slides along the length of the core on which wire is wrapped with the help of shafts. Shafts are fixed parallel to core to facilitate movement of slider. Tip of the slider consists of a conductive material or a piece of metal which remains in contact with the wire wrapped around core. One output lead is connected to slider and another lead is taken from one of the extreme ends of resistive wire. As slider moves towards the end from where out put lead is taken out, length of resistive path is decreased and hence the resistance also decreases. Similarly, when slider moves away, length of resistive path increases which increases the resistance. In this way, resistance value is increased or decreased by moving slider along the core.

POTENTIOMETERS 

     These are variable resistors. Potentiometers may be made to take analog readings as well as readings in discrete steps. Various resistance values are obtained by a slider arm. One end of the slider arm is fixed for any eccentric or linear movements and only allowed to rotate at its axis. Another end remains in contact with the circular resistive path made on flat surface. Resistive path of potentiometers can be made by depositing layers of resistive materials onto a surface of non-conductive material or it can be made using wire by wrapping around a core like Rheostats. The only different between Rheostat and wire wound potentiometer is that core is not straight like a bar. In wire-wound potentiometers core is bend in such a way that it makes a circular path for slider. Slider can be made to move in discrete steps or it can be made to move continuously in a circular path.

LIGHT DEPENDENT RESISTORS (LDRs) 

     These are variable resistors. Resistance of LDRs varies with variation in light striking it. When light intensity striking LDR falls, its resistance increase and vice versa. LDRs are used in camera to switch ON flash in automatic mode while capturing pictures in low lights and also they are used to control street lights for automatic switching ON and OFF to save power consumption. LDRs also called Photo-resistors.

THERMISTORS  

     These are variable resistors. Resistance of Thermistors varies with variation in temperature of the atmosphere surrounding it. Both positive temperature coefficient (PTC) and negative temperature coefficient (NTC) substances are used in construction of Thermistors. Resistance of PTC Thermistors increases with increase in temperature and vice versa. On the other hand, resistance of NTC Thermistors decreases with increase in temperature and vice versa. Thermistors can be used to protect circuits from over current and they can be used in appliances like electrical geysers, electrical hotplates, etc., to protect overheating and damage to man and machine.

COLOR CODING OF RESISTORS

Following table is used to know the value of color bands of resistors ;

Following method is used to calculate resistance value from the colour bands of resistors using colour coding table given above ;

For example, we take resistor given below and calculate its value using colour bands ;

1. First band of resistor is Yellow ; Value of Yellow is 4,
2. Second band of resistor is Violet ; Value of Violet is 7,
3. Third band of resistor is Black ; Value of Black is 1,
4. Fourth band of resistor is Gold ; Value of Gold is 5%,
5. Write down value of first band i.e., 4,
6. Write down value of second band i.e., 7,
7. From first and second bands, we obtained digit 47,
8. Third band is multiplier band and value of third band is 1,
9. After multiplication, we obtained figure 47,
10. Calculate 5% of figure obtained from first, second & third bands i.e., 2.35,
11. We obtained value of above resistor as 47 Ω  +/- 2.35 Ω.

Let's take one more example of resistor given below and calculate its value using colour bands ;

1. First band of resistor is Red ; Value of Red is 2,
2. Second band of resistor is Black ; Value of Black is 0,
3. Third band of resistor is Brown ; Value of Brown is 10,
4. Fourth band of resistor is Gold ; Value of Gold is 5%,
5. Write down value of first band i.e., 2,
6. Write down value of second band i.e., 0,
7. From first and second bands, we obtained digit 20,
8. Third band is multiplier band and value of third band is 10,
9. After multiplication, we obtained figure 200,
10. Calculate 5% of figure obtained from first, second & third bands i.e., 10,
11. We obtained value of above resistor as  200 Ω  +/- 10 Ω.

SELECTION OF RESISTORS

Selection criterion of Resistors consists of three most important factors given below ;

1. Resistance value,
2. Wattage Rating, &
3. Tolerance / Precision

RESISTORS IN SERIES

     In circuits of resistors connected in series, voltage drops across each resistor and this voltage drop depends upon value of resistors. For example ;

Vtotal = V1 + V2                                                   .... (i)

As per Ohm's law ;

I = V/R

Or, V = I . R                                                 .... (ii)

Therefore, putting values of equation (ii) & in equation (i), we  get ;

Itotal . Rtotal = I1 . R1  + I2 . R2                .... (iii)

Or, Rtotal = R1 + R2                                       .... (iv)

                                                                                        (because Itotal = I1 = I2, as value of current remains

                                                                         same because there is only one path for flow of current)

R_total = R₁ + R₂ + R₃ + ........... + R_n          (universal form of equation (iv) for 'n' number of 

                                                                         resistors in series)

RESISTORS IN PARALLEL

     When resistors are connected in parallel with each other, current then have more than one path to flow through circuit as we can see in figure below ;

Therefore, 

Itotal = I1 + I2                                               .... (i)

As per Ohm's law ;

I = V/R                                                         .... (ii)

Therefore, putting value of equation (ii) in equation (i), we get equation (iii),

Vtotal /Rtotal = V1/R1 + V2/R2                   .... (iii)

Or, 1/Rtotal = 1/R1 + 1/R2                               .... (iv) 

                                                                                        (because Vtotal = V1 = V2, as value of voltage remains same)

Or Rtotal = (R1 . R2) / (R1 + R2)

When all the resistors connected in parallel are of same value, then total resistance will be ;

Rtotal = Resistor Value of One Resistor / Number of Resistors

RESISTORS CONNECTED IN SERIES-PARALLEL COMBINATIONS 

     Complex circuits have resistors connected in series and as well as parallel. Those circuits are reduced to simplify by first calculating resistance of two or more resistors either connected in series or parallel. For example, we take below circuit and calculate resistance ;

     In above problem, it can be observed from figure that resistors R2 & R3 are connected in parallel. First we will reduce circuit by calculating resistance value of these two resistors as given below ;

     We know that formula for calculating resistance of resistors connected in parallel is ;

R4 = (R2 . R3) / (R2 + R3)                        

We get R4 and circuit can now be drawn to simplest form as given below ;

    Now, it can be observed from above figure that resistors R1 & R4 are connected in series and there resistance can be calculated as given below ;

Therefore, Rtotal = R1 + R4