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EXP NO: 1 LINEAR VARIABLE DIFFERENTIAL TRANSFORMER (DISPLACEMENT TRANSDUCER) AIM: To obtain the characteristics of LVDT APPARATUS REQUIRED: LVDT kit, Multimeter, Power supply. THEORY: LVDT is an inductive transducer used to convert linear displacement in to electrical signals. The transformer consists of a single primary winding P and two secondary windings S1 and S2 wound on a cylindrical former. The secondary windings have equal number of turns and are identically placed on either side of primary winding. The primary winding is connected to an alternating current source. A movable soft iron core is placed inside the former. The displacement to be measured is applied to the arm attached to the soft iron core. The core is made of high permeability nickel iron which is hydrogen annealed. This gives low harmonics, low null voltage and a high sensitivity. This is slotted longitudinally to reduce eddy current losses. The assembly is placed in stainless steel housing and the end lids provide electrostatic and electromagnetic shielding. The frequency of ac voltage applied to the primary windings may be between 50 Hz to 30 KHz. Since the primary winding is excited by an alternating current source, it produces an alternating magnetic field, which in turn induces alternating voltages in the two secondary windings. The output voltage of secondary S1 is ES1 and S2 is ES2.In order to convert the outputs from S1 and S2 in to a single voltage signal, the two secondaries S1 and S2 are connected in series opposition. Thus the output voltage of the transducer is the difference of the two voltages. Differential output voltage PROCEDURE: E0 = ES1-ES2 1. Connections are given as per the circuit diagram. 2. By varying the displacement given by screw gauge, the differential output voltage is noted at secondary coil side. 3. The output voltages are noted for both positive and negative displacements. 4. Then a graph is plotted against voltage and displacement RESULT: Thus the characteristics of Displacement transducer LVDT is obtained and the residual voltage is determined. EXP NO: 2 STUDY OF PRESSURE TRANSDUCER - BOURDON GAUGE AIM: To study the operation of Bourdon tube – pressure transducer and to draw its characteristics APPARATUS REQUIRED: Bourdon pressure transducer kit, Multimeter Foot pump THEORY: The Bourdon tubes are made out of an elliptically flattened tube bent in such a way to produce C type, spiral, twisted tube and helical shapes. One end of the tube is sealed and other end is open for the fluid to enter. When the fluid whose pressure is to be measured enters the tube, the tube tends to straighten out on account of the pressure applied. This causes a movement of the free end. The displacement of the free end is amplified through mechanical linkages. The amplified displacement is used to move a pointer on a scale calibrated in terms of pressure or may be applied to a electrical displacement transducer whose output may be calibrated in terms of the pressure applied. ADVANTAGES 1. Bourdon tubes are used for measuring high range of pressure. 2. They can be easily adapted foe designs for electrical outputs. 3. Good accuracy except at low pressures. DISADVANTAGES 1. Bourdon tubes have low spring gradient which limits their use up to a pressure measurements of 3 MN/m3 2. Bourdon tubes are susceptible to shocks and vibrations. PROCEDURE: 1. Connect Bourdon tube to pressure kit. 2. Release the pressure in the foot pump and Bourdon tube by opening the valve. 3. Close the valve in both foot pump and Bourdon tube. 4. Using foot pump apply the pressure and note down the corresponding pressure readings and displacement readings. 5. Measure the output voltage using multimeter 6. Tabulate the readings and plot the graph between gauge pressure and output voltage. RESULT: Thus the operation of bourdon tube as a transducer is studied and the characteristics are drawn. EXP NO: 3 MAXWELL’S INDUCTANCE BRIDGE AIM: To find the value of unknown inductance and Q factor of the coil using Maxwell’s inductance bridge. APPARATUS REQUIRED: S.NO 1. 2. 3. 4. 5. 6. 7. 8. Component Maxwell’s bridge trainer kit Unknown inductance Decade resistance box Breadboard Headphone Decade Inductance box Audio oscillator Digital multimeter Quantity 1 1 1 1 1 1 1 1 FORMULAE: Inductance (Lx) = R2R3C1 Henry Resistance (Rx) = R2R3/R1 ohms Q factor (Q) = Lx/Rx % error = Actual value – Measured value --------------------------------------Actual value * 100 THEORY: In this bridge, an inductance is measured by comparison with a standard variable capacitance Let, Lx = Unknown inductance Rx=effective resistance of inductance Lx R1, R2, R3 =Known non inductive resistances C1 = variable standard capacitor At balance, (R1+jL)(R1/1+jR1C1)=R2R3 RxR1+jLxR1=R2R3+jR1C1R2R3 Equating the real &imaginary parts RxR1= R2R3 R2 Rx = R3 R1 ; LxR1 = R1R2R3C1 Lx = R2R3C Lx Q= Rx = R1 C1 Maxwell’s inductance bridge is very useful for measurement of a wide range of inductance at power and audio frequencies. This bridge is limited to measurement of low Q coils. This bridge is also unsuited for coils with a very low value of Q.So maxwell’s bridge is suited for measurement of only medium Q coils. The advantage of this bridge is that the frequency does not appear in any of the two balance equations. The two balance equations are independent if R1 and C1 are chosen as variable elements. PROCEDURE: i) ii) iii) iv) v) The connections are made as shown in figure. Output of the trainer kit is connected to the digital multimeter. Power supply is switched “ON” and LX value is set. R1 and R3 are adjusted to get null balance condition. The values of resistance R1 and R3 are then measured values are noted and tabulated. RESULT: Thus the value of unknown inductance is found using Maxwell’s inductance bridge. OBSERVATION: TABLE-1 R1 (K) S.NO R2 (K) R3 (K) C1 (F) Lx (H) Rx (K) Q-factor TABLE-2 S.NO Actual Value (H) Measured Value (H) Percentage error (%) SCHERING’S BRIDGE EXP NO: 4 AIM: To measure the value of unknown capacitor using Schering’s bridge. APPARATUS REQUIRED: S.No Component 1. Schering’s Bridge trainer kit Quantity 1 2. Digital multimeter 1 3. Decade capacitance box 1 4. Patch cords FORMULAE: Capacitance (CX) =C3 R1 R4 Resistance C1 Rx = R2 Ohms C3 Dissipation factor = CX RX = fd Actual value –Measured value % error = ________________________ *100% Actual value THEORY: Schering Bridge is widely used for capacitance and dissipation factor measurement. It is used in the measurement of the properties of insulator, Capacitors, bushings, insulating oil and other insulating materials. Let Cx =Capacitor whose capacitance is to be measured. Rx = A series resistance representing the loss in the capacitor Cx R2 = A non-inductive resistance C3 =A standard capacitor C1 = A variable capacitor R1 = A variable non-inductive resistance in parallel with variable capacitor C1. At balance, 1 R1 R2 (Rx +-------- (----------------) = ---------jCx 1+jC1 R1 jC3 R1 R2 R1R2C1 R1Rx +------ = -------- + -----------jC jC C3 Equating the real and imaginary parts R1R2C1 RxR1 = ---------C3 Rx fd R1 R2 ------ = ------Cx C3 R2 R1 = --------C1 ; = Cx ------- C3 C3 R2 = Cx R1 C1 R1 (R2 -----) (-------C3) = R1 C1 C3 R2 The equations for capacitance shows that since R1 and C3 are fixed, the dial of resistor R2 may be calibrated to read the fd directly. Since C1 is a variable decade capacitor box, its setting in microfarad directly gives the value of the fd. = PROCEDURE: 1.The connections are made as per the circuit diagram. 2. The digital multimeter is connected across the output of the trainer kit. 3.The power supply is switched “ON”, capacitor C1 is kept at maximum or minimum position. Potentiometer of R1 is adjusted to get null balance in multimeter. 4. The values of resistance R1 and R2 are measured. 5.Cx values are calculated and tabulated. RESULT: Thus the value of unknown capacitance is found using Schering’s bridge. TABLE-1 S.NO R1 R2 C1 C2 Cx Rx Units F F F TABLE-1 S.NO Units Actual Value (F) F Measured Value (F) F Percentage error (%) % fd EXP NO: 5 WHEATSTONE’S BRIDGE AIM: To measure the value of unknown resistor using Wheat stone’s bridge. APPARATUS REQUIRED: S.No 1. Component Regulated power supply(0-15)V Qty 1 2. Bread Board 1 3. Resistors 1 K 2 4. Decade resistance box 1 5. Digital Multimeter 1 6. Connecting Wires - FORMULAE: R1 Resistance (Rx) =----- R3 ohms R2 Actual value-Measured value % error= ------------------------------------- *100 Actual value THEORY : A very important device used in the measurement of medium resistance is the Whetstone’s bridge. It is an accurate and reliable instrument and its extensively used in industry. It has four resistive arms, consisting of resistances P,Q,R,S, together with a source of emf and a null detector, usually a galvanometer G or other sensitive current meter. The current through the galvanometer depends on the potential difference between points b and d. The bridge is said to be balanced when there is no current through the galvanometer or when the potential difference across the galvanometer is zero. This occurs when the voltage from point ‘b’ to point ‘a’ equals the from point’d’ to ‘a’ or by referring to the other battery terminal when the voltage from point ‘d’ to point ‘c’ equals the voltage from points ‘b’ to point ‘c’. At balance I1 R1 = I2 Rx I1 = I3 E / (R1+R2) I2 =I4 =E / (Rx+R3) Where, E is the emf of the battery R1 / (R1+R2) = Rx / (Rx+R3) R2 Rx = R1 R3 Rx= R1 R3 / R2 ohms Here unknown resistance Rx is called the standard arm and R1 , R2 are Called ratio arms. Hence Whetstone’s bridge is an instrument for making comparison measurements and operates upon a null indication principle. PROCEDURE: i) ii) iii) iv) v) vi) vii) Connections are made as shown in figure. Set the value of R1 and R2 as known reference value. Galvanometer is connected as detector. Power supply is switched on. R3 is adjusted using DRB to set null balance in the detector. Then, the values of unknown resistance Rx are calculated. Similarly, various resistance values are noted and tabulated. RESULT: Thus the value of unknown resistance is found using wheat stone’s bridge. OBSERVATION: TABLE-1 R1 (K) S.NO R2 (K) R3 (K) R1 R3/ R2 TABLE-1 S.NO Actual Value (K) Measured Value (K) R1 Resistance (Rx) =----- R3 R2 Actual value-Measured value % error= ------------------------------------- *100 Actual value Percentage error (%) Rx (K) MEASUREMENT OF RESISTANCE USING KELVIN’S DOUBLE BRIDGE EXP NO: 6 AIM: To measure the unknown resistance using Kelvin’s double bridge . APPARATUS REQUIRED: S.No. 1. Component Kelvin’s double bridge trainer kit Qty 1 2. Unknown Resistors 5 3. Galvanometer 1 4. Connecting wires 1 FORMULAE: P Resistance R = ----- *S Q Actual value-Measured value % error= ------------------------------------- *100 % Actual value THEORY: The Kelvin double bridge incorporates the idea of a second set of ratio arms hence the name double bridge and the use of four terminal resistors for the low, resistance arms. The first of the ratio arms is P and Q. The second set of ratio arms,P and Q is used to connect the galvanometer to a point d at the appropriate potential between points m and n to eliminate the effect of connecting lead of resistance ‘r’ between the known resistance, R and the standard Resistance S. The ration p/q is made equal to p/q under balanced conditions there is no current through the galvanometer. p Now, Eab = -------- Eac P+Q (p+q) r Eac = I R+S+ P+q+r and P Eamd = I (p+q) r R + P+q p+q+r pr =I R+ P+q+r For zero galvanometer deflection, Eab, =Eamd P (p+q)r I R+S+ P+q p+q+r pr =I R+ p+q+r P R= qr P p+q+r Q S+ Q p q Then unknown resistance, R=P/Q*S It indicates that resistance of connecting lead, r has no effect on the measurement, provided that the two sets of ratio arms have equal ratios. It indicates that it is desirable to keep r as small as possible in order to minimize the errors in case there is a difference between ratios P/Q and p/q. PROCEDURE: 1. The connections are made as per the circuit diagram. 2. Connect the unknown resistance between the terminal a and m. 3. Balance the bridge by adjusting the standard resistance S. Then the value of ‘S’ is noted from which the value of unknown resistance R is found. 4. Repeat the above procedure for various values of unknown resistors RESULT: Thus the value of unknown resistance is calculated using Kelvin’s double bridge. TABLE-1 P Q S P/Q R (K) (K) (K) S.NO Units TABLE-2 S.NO Actual Value Measured Value Units Percentage error (%) % CALCULATION: P i) R = ----- *S = Q Actual value-Measured value ii)% error= ------------------------------------- *100 % Actual value EXP NO: 7 POWER MEASUREMENTS IN THREE PHASE CIRCUITS AIM: To measure the three phase power using two wattmeter method and also to find out the power factor. NAME PLATE DETAILS: 3 Load Auto Transformer Fuse Rating: 125% of rated current (full load current) APPARATUS REQUIRED: S.No 1. 2. 3. 4. 5. Name of the Apparatus Ammeter Voltmeter Wattmeter Three phase load 3 phase auto transformer Type MI MI UPF /Y Range (0-10A) (0-600V) (500V-10A) Quantity 1 1 2 1 1 FORMULAE: 1. Total Power (W=W1+W2) in Watts. Where W1, W2-Wattmetter readings. 2. (i) Power factor (Cos) = W1+W2 3 VL IL (ii) Power factor (Cos) = Cos tan-13 (W1W2) W1+W2 3. Total power W = 3 VL IL Cos in Watts Where VL, IL are load voltage and load current respectively PRECAUTION: (i) (ii) At the time starting the loading rheostat should be at no load condition. Autotransformer should be at minimum position at the time of starting. PROCEDURE: (i) Connections are given as per the circuit diagram. (ii) The rated voltage is given by adjusting the autotransformer. (iii) The meter readings are noted down at no load condition. (iv) By applying the load gradually the corresponding meter readings are noted down. (v) The load is released gradually and the supply is switched off. MODEL CALCULATION: GRAPH: The graph are drawn as (i) Load Current Vs Total power (ii) Load Current Vs Power Factor RESULT: Thus the three phase power and power factor are measured using two wattmeter method. EXP NO: 8 CALIBRATION OF CURRENT TRANSFORMER AIM: To study the working of current transformer and to verify its operation. APPARATUS REQUIRED S.No 1. 2. 3. 4. 5. Name of the Apparatus Current transformer Ammeter Loading transformer 1 phase auto transformer Connecting wires Type Range MI (0-100A),(0-5)A Quantity 1 Each 1 1 1 THEORY Current transformers (CT) are used for the measurement of large Current. Use of CT avoids the use of high range meters. CT is actually a step up transformer which steps down the current therefore small range ammeter can be used for the current measurement. The primary winding of CT is connected in series with the line or load carrying the current which has to be measured. The primary winding consists of very few turns and therefore there is no appreciable drop. The secondary winding Consists of large number of turns. The ammeter is connected across the secondary to measure the current. The load current is calculated from the reading of the ammeter. Load current =Primary winding current k X Ammeter reading (Secondary Current) No. of turns in Secondary Where k is turns ratio = No. of turns is primary Procedure 1. Connections are given as per the Circuit diagram 2. Measure the input primary current and secondary current 3. Vary the load and measure current 4. Draw the curve for primary and secondary current. Result: Thus the calibration of current transformer is studied. The error is calculated and the graph is plotted. EXP NO: 9 ANALOG TO DIGITAL CONVERTER AIM: To design an analog to digital converter and to verify the output . APPARATUS REQUIRED: S.No. 1. Component IC 358 Qty 3 2. IC7404,IC 7486 Each 1 3. IC 7408 2 4. Resistors 2.2K 4 5. Digital trainer kit 1 6. Regulated power supply (0-30V) 1 7. Bread board 1 8. Connecting wires As required THEORY: The flash ADC is also known as the parallel comparator ADC and is the fastest and the most expensive one. The circuit has a resistive divider network, 4 op-amps comparators and 4 line to 2 line priority encoder. The comparator is built in such a way That a little hysteresis is built into the comparator to resolve any problems while both the inputs are equal. Now,, comparison voltage is available at each node of the resistive divider. All the resistor are of equal value. Therefore the voltage levels available are Equally divided between VR and the ground the circuits compare analog input voltage Va and the ground. VR and the ground. The circuits compare analog input voltage Va with each of the node voltages. The conversion takes place simultaneously instead of sequentially; therefore the circuit has high speed. The typical conversion time is 100ns. The conversion time is restricted only by the speed of the comparator and of the priority encoder. The disadvantage is the number of comparators needed almost doubles for each added bit. The general formula is the number of comparators needed are (2n -1,) where n is the desired number of bits. PROCEDURE: 1. 2. Connections are given as per the circuit diagram. Vary the input voltage by RPS and note down the binary value by sensing the glow of LED RESULT: Thus an analog to digital converter is designed and the output is verified EXP NO: 10 DIGITAL TO ANALOG CONVERTER (R-2R LADDER NETQWORK) AIM: To construct a digital to analog converter and to verify the output. APPARATUS REQUIRED: S.No. 1. Component IC 741 Qty 1 2. Resistor 10K 4 3. Resistor 20K 6 4. Resistor 100 ohms 1 5. Digital trainer kit 1 6. Regulated power supply (0-30V) 1 7. Bread board 1 8. Voltmeter (0-10)V 1 Connecting wires As required THEORY: A4 bit R-2R ladder network is shown. Each digital input controls the position of its corresponding current switch. A current switch steers its ladder, current either into a real ground (position 0) or a virtual ground (position 1). Thus the wiper of each switch is always at ground potential. So that the rung current are constant except for the brief transition time of each switch. In circuit a rail current flow horizontally rang current flow down through the bit switches. The rail current 1, enters node 0,where it sees a resistance Ro, Ro is the equivalent of a 2R resistor via switch Do to ground in parallel with a 2R terminate resistor. Thus Ro =2R112R=R. As rail current /1 leave node it sees R in series with R in series with Ro=R or 2R. If we work our way back from the terminate end of the voltage source, the value of resistance looking into a node is R.R. is called the characteristic resistance of the ladder network In other words, Vref sees the entire ladder network as the single resistor equal to R. Since Vref =sees the ladder network as a resistance R, rail current I ref is I ref =V ref/R The current Iref splits into 2 equal parts at node 3. The rung current and rail current are I3 = I ref /2. Each rail current devices equally again at each nodes as it proceeds down the ladder. Thus, I3=I ref /2, I2=I3/2 I ref / 4, I1=I2/2 I ref / 8, U0=I2/2 = I ref / 16, I0 is the current controlled by the LSB switch. To write the output /input equation for the ladder network, we observe that Iout is the sum of all the rungs current steered into the output by the bit switches. Iout =I0*D, where D =decimal value of the digital input. The output ladder current can be converted into voltage by adding an op-amp and a feedback resistor. Output voltage Vo is given by Vo= Iout Rp PROCEDURE: 1. Circuit connections are made as per the circuit diagram. 2. Connect the digital input D0 , D1 ,D2 ,D3 to +5V or ground , according to the required binary input.(+5V represents logic 1 and GND represents logic 0). 3. Observe the output through a multimeter for each sequence and note down the values for each sequence. 4. Calculate the theoretical output using the formula V0=Vref/23*( D0 20+D121+D222+D323) 5. Verify the measured and calculated output. RESULT: Thus a digital to analog converter is designed and the output is verified EXP NO: 11 STUDY OF TRANSIENTS AIM: To study the transient operation of the following circuits • Series Circuit • RC Series Circuit • RLC Series Circuit Apparatus Required: • Series AC and DC Circuit trainer (TST-06) • DC.Ammeter (0-200mA) • Dual trace CRO -20MHz • Patch chords (or) wires Procedure RL Series Circuit Connect output or square wave generater to input of RL circuit Connect 0 to 80% of inductive value to inductor point of RL Circuit Connect DC Ammeter to RL Circuit Connect DC Ammeter to RL Circuit Connect CRO Probe across the resistor R in RL Circuit Switch on the CRO Connect 230 V Supply to trainer Observe the exponential waveform in the CRO RC Series Circuit Connect output or square wave generater to input of RC circuit Connect IMFD / 50VCapacitor to capacitor point of RC Circuit Connect DC Ammeter to RL Circuit Connect DC Ammeter to RL Circuit Connect CRO Probe across the resistor R in RL Circuit Switch on the CRO Connect 230 V Supply to trainer Observe the exponential waveform in the CRO RLC Series Circuit Connect output or square wave generater to input of RLC circuit Connect 0 to 80 of inductive value to inductor point of RLC Circuit Connect IMFD / 50VCapacitor to capacitor point of RLC Circuit Connect DC Ammeter to RLC Circuit Connect CRO Probe across the resistor R2 in RLC Circuit Switch on the CRO Connect 230V Supply to trainer Observe the inverse exponential waveform in the CRO RESULT: Thus the transient response of various DC transient circuits was studied and the characteristic curves were plotted. EXP NO: 12 INSTRUMENTATION AMPLIFIER AIM: To construct an instrumentation amplifier and to find out the gain. COMPONENTS REQUIRD: S.No Apparatus 1. OP-AMP IC 741 2. Resisters 3. Multimeter 4. RPS 5. Bread board 6. Connecting wires Range 1K Quantity 3 7 1 0-30V 2 1 THEORY: An instrumentation amplifier is a type of differential amplifier that is outfitted with input buffers, which eliminate the need for input impedance matching and thus make it particularly suitable for use in measurement and test equipment. Additional characteristics include very low DC offset, low drift, low noise, very high open loop gain, very high common mode rejection ratio and very high input impedances. PROCEDURE: 1. 2. 3. Give the connections as per the circuit diagram. Imbalance the bridge by adjusting the 1K EXP NO: 13 CALIBRATION OF SINGLE PHASE ENERGY METER USING PHANTOM LOADING AIM: To Calibration of single phase energy meter using phantom loading. APPARATUS REQUIRED; S.No Name of apparatus Range type quantity 1. Energy meter 1 2. voltmeter 0-300V MI 1 3. Ammeter 0-10A MI 1 4 Watt Meter 300V, 10A UPF 1 5 1: auto Transformer 6 Stop Watch FORMULAE: Energy meter constant 1200 rev /KWhr Energy conserved for 1 rev = 3KWsec Energy conserved for 3 rev = 9 KW sec % of error = calculated reading-observed reading Calculated reading THEORY: Energy meter has its own characteristics constant specified by the manufacturer which relates the energy measured in joules and the number of revolution of the disc. For various loads, the time required to complete 3 revolutions of disc is measured with the help of stop watch, using current, is calculated for calibration purpose. PROCEDURE: 1. 2. 3. 4. 5. 6. 7. Give connections as per the circuit diagram Switch on the supply for auto transformer Vary the auto note down the corresponding values of voltmeter, ammeter and wattmeter. Note down the twice taken for 3 or 5 revolutions Replay steps 3&4 for the rates current Calculate the true energy, measured energy and percentage of error. Draw the graph between percentages of error and load current. RESULT: Thus the single phase energy mete using phantom loading is calibrated and the graph is plotted. TABULATION S.no Voltmeter Reading (V) Ammeter Reading (A) Time for 3 rev (s) Calculated reading (W sec) Observed reading (Wsec) % of error EXP NO: 14 MEASUREMENT OF IRON LOSS AIM: To measure iron loss of given ring specimen. APPARATUS REQUIRED: S.No Apparatus 1. Maxwell’s Inductance bridge 2. Multimeter 3. Patch Cords Quantity 1 1 FORMULA USED: At unbalanced position unknown inductance =Std R2 *Std R3 *C Rs= Std R1 *Std R3 R2 Iron loss = IL2 * (Rs-Rw) R1= R2 * R3 R4 THEORY: A number of bridge circuits may be used for measurement of iron loss and a.c. permeability. They are not only useful where materials work at low flux densities, but also where only small quantity of material is available for testing and the test is to be carried out at commercial or audio frequencies. In this case Maxwell’s inductance bridge is used. PROCEDURE: 1. Connections are given as per the circuit diagram. 2. Connect the ring specimen to the bridge arm for which the measurement is to be made. 3. Switch on the bridge circuit and measure the output using a multimeter. 4. Find out the iron loss of the given specimen using the formula. 5. Repeat the same procedure for different ring specimens. RESULT: Thus the iron loss of given ring specimen is calculated.