Verification of Kirchhoff's Laws & Theorems in Electrical Circuit Experiments, Exams of Engineering

Download Verification of Kirchhoff's Laws & Theorems in Electrical Circuit Experiments and more Exams Engineering in PDF only on Docsity! 1 LABORATORY MATERIAL EE0211 – ELECTRICAL CIRCUITS LAB DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING FACULTY OF ENGINEERING & TECHNOLOGY SRM UNIVERSITY, Kattankulathur – 603 203 2 CONTENTS Sl.No. Name of the Experiments Page No. 1 Verification of Kirchoff’s laws 3 2 Verification of Superposition theorem 6 3 Verification of Thevenin’s & Norton’s Theorem 9 4 Verification of Maximum Power Transfer theorem 15 5 Power measurement in 3 phase unbalanced circuits 19 6 Power measurement in 3 phase balanced circuits 20 7 Power measurement using 3 voltmeter & 3 ammeter method 22 8 Circuit analysis using CRO 26 9 Circuit transients by digital simulation 28 10 Study of resonance 30 5 KVL - Practical Values Sl.No. RPS Voltage KVL E1 = V1 + V2 E1 E2 V1 V2 V3 V V V V V V 1 5 5 0.6 4.4 0.56 5 2 10 10 1.13 8.83 1.19 9.96 3 15 15 1.72 13.20 1.78 14.92 Model Calculations: Result: Thus Kirchoff’s voltage load and Kirchoff’s current law verified both theoretically and practically. 6 Experiment No. 2 Date : VERIFICATION OF SUPERPOSITION THEOREM Aim: To verify the superposition theorem for the given circuit. Apparatus Required: Sl.No. Apparatus Range Quantity 1 RPS (regulated power supply) (0-30V) 2 2 Ammeter (0-10mA) 1 3 Resistors 1k, 330, 220 3 4 Bread Board -- -- 5 Wires -- Required Statement: Superposition theorem states that in a linear bilateral network containing more than one source, the current flowing through the branch is the algebraic sum of the current flowing through that branch when sources are considered one at a time and replacing other sources by their respective internal resistances. Precautions: 1. Voltage control knob should be kept at manimum position 2. current control knob of RPS should be kept at maximum position Procedure: 1. Give the connections as per the diagram. 2. Set a particular voltage value using RPS1 and RPS2 & note down the ammeter reading 3. Set the same voltage in circuit I using RPS1 alone and short circuit the terminals and note the ammeter reading. 4. Set the same voltage in RPS2 alone as in circuit I and note down the ammeter reading. 5. Verify superposition theorem. 7 CIRCUIT - 1 CIRCUIT - 2 CIRCUIT - 3 TABULAR COLUMN Theoretical Values RPS Ammeter Reading (I) mA 1 2 Circuit – 1 10 V 10 V I = 8.83 Circuit – 2 10 V 0 V I’= 3.5 Circuit – 3 0 V 10 V I”= 5.3 I = I’  I” = 8.83 Practical Values RPS Ammeter Reading (I) mA 1 2 Circuit – 1 10 V 10 V I = 8.5 Circuit – 2 10 V 0 V I’= 3.5 Circuit – 3 0 V 10 V I”= 5 I = I’  I” = 8.5 mA = 3.5 + 5 = 8.5 mA 10 Circuit - 1 : To find load current To find VTH To find RTH Thevenin’s Equivalent circuit: 11 Model Calculations: Result: Hence the Thevenin’s theorem is verified both practically and theoretically 12 Experiment No. 4 Date : VERIFICATION OF NORTON’S THEOREM Aim: To verify Norton’s theorem for the given circuit. Apparatus Required: Sl.No. Apparatus Range Quantity 1 Ammeter (0-10mA) MC (0-30mA) MC 1 1 2 Resistors 330, 1K 3,1 3 RPS (0-30V) 2 4 Bread Board -- 1 5 Wires -- Required Statement: Any linear, bilateral, active two terminal network can be replaced by an equivalent current source (IN) in parallel with Norton’s resistance (RN) Precautions: 1. Voltage control knob of RPS should be kept at minimum position. 2. Current control knob of RPS should be kept at maximum position. Procedure: 1. Connections are given as per circuit diagram. 2. Set a particular value in RPS and note down the ammeter readings in the original circuit. To Find IN: 3. Remove the load resistance and short circuit the terminals. 4. For the same RPS voltage note down the ammeter readings. To Find RN: 5. Remove RPS and short circuit the terminal and remove the load and note down the resistance across the two terminals. Equivalent Circuit: 6. Set IN and RN and note down the ammeter readings. 7. Verify Norton’s theorem. 15 Experiment No. 5 Date : VERIFICATION OF MAXIMUM POWER TRANSFER THEOREM Aim: To verify maximum power transfer theorem for the given circuit Apparatus Required: Sl.No. Apparatus Range Quantity 1 RPS (0-30V) 1 2 Voltmeter (0-10V) MC 1 3 Resistor 1K, 1.3K, 3 3 4 DRB -- 1 5 Bread Board & wires -- Required Statement: In a linear, bilateral circuit the maximum power will be transferred to the load when load resistance is equal to source resistance. Precautions: 1. Voltage control knob of RPS should be kept at minimum position. 2. Current control knob of RPS should be kept at maximum position. Procedure: Circuit – I 1. Connections are given as per the diagram and set a particular voltage in RPS. 2. Vary RL and note down the corresponding ammeter and voltmeter reading. 3. Repeat the procedure for different values of RL & Tabulate it. 4. Calculate the power for each value of RL. To find VTH: 5. Remove the load, and determine the open circuit voltage using multimeter (VTH) To find RTH: 6. Remove the load and short circuit the voltage source (RPS). 7. Find the looking back resistance (RTH) using multimeter. Equivalent Circuit: 8. Set VTH using RPS and RTH using DRB and note down the ammeter reading. 9. Calculate the power delivered to the load (RL = RTH) 10. Verify maximum transfer theorem. 16 Circuit - 1 To find VTH To find RTH Thevenin’s Equation Circuit 17 Power VS RL Circuit – I Sl.No. RL () I (mA) V(V) P=VI (watts) 1 2 3 4 5 6 7 8 200 400 600 800 1200 1300 1400 1500 1.3 1.2 1.1 1 0.80 0.77 0.74 0.71 0.27 0.481 0.638 0.771 1.083 1.024 0.998 0.968 0.26 0.53 0.707 0.771 0.866 0.788 0.738 0.687 To find Thevenin’s equivalent circuit VTH (V) RTH () IL (mA) P (milli watts) Theoretical Value 2002 1320 0.758 0.759 Practical Value 2 1306 0.77 0.77 20 for resistive load Formulae Used: 1. Real power = w1 + w2 2. Reactive power = )(3 21 ww  3. Tan  = 21 21 )(3 ww ww   4. Power factor = cos  Two Wattmeter Method : Resistive Load V (volt) I (A) MF = Wattmeter Reading (W1) MF = Wattmeter Reading (W2) Power Cos  OBS (watt) ACT = OBS X MF (watt) OBS (watt) ACT=OBS x MF (watt) Real Power (watt) Reactive power (watt) 460 460 460 460 460 460 460 460 460 0 1.8 3.7 4.6 5.5 6.3 7.2 8.1 9 0 70 160 200 240 280 320 350 390 0 560 1280 1600 1920 2240 2560 2800 3120 0 90 180 210 250 290 330 370 410 0 720 1440 1680 2000 2320 2640 2960 3280 0 1280 2720 3280 3920 4560 5200 5760 6400 0 -277.12 -277.12 -138.56 -138.56 -138.56 -138.56 -277.12 -277.12 0 0.977 0.9949 0.999 0.9 0.993 0.996 0.9988 0.990 21 Two Wattmeter Method : Inductive Load V (volt) I (A) MF = Wattmeter Reading (W1) MF = Wattmeter Reading (W2) Power Cos  OBS (watt) ACT = OBS x MF (watt) OBS (watt) ACT=OBS x MF (watt) Real Power (watt) Reactive power (watt) 410 410 410 410 410 410 1 2 3 4 5 6 11 15 28 43 78 95 89 120 140 344 624 760 26 32 53 80 106 132 208 256 424 640 848 1056 296 376 564 984 1472 1816 -554.26 -443.41 -734.39 -1108.51 -1461.78 -1829.05 0.351 0.647 0.609 0.664 0.708 0.705 Model Calculations: Result: Thus power for three phase power supply was measured using 2 wattmeter method. 22 Experiment No. 7 Date : POWER MEASUREMENT BY 3 - VOLTMETER Aim: To measure the power in an inductive circuit, Eg: transformer, by 3- voltmeter method. Apparatus Required: Sl.No. Apparatus Range Quantity 1 Ammeter (0-5A) MI 1 2 Voltmeter (0-150V) MI (0-300V) MI 2 1 3 Transformer 230V/115V, 1KVA 1 4 Auto Transformer - - 5 Auto Transformer - 1 6 Rheostat 100 1 Precaution: 1. The DPST switch must be kept open initially. 2. The auto transformer must be kept at minimum potential position 3. The rheostat must be kept at maximum resistance position. Procedure: 1. Give the connections as per the circuit diagram. 2. Adjust the auto transformer, to bring the rated voltage of the transformer 3. Note down the transformer and voltmeter readings. 4. Vary the rheostat for different values and note down the corresponding meter readings. 3 – Voltmeter Method Sl. No. I (amp) Vs (volts) VR (volts) VL (volts) P (watts) Cos  1 2 3 4 5 6 0.2 0.6 0.8 1 1.1 1.2 150 150 150 150 150 150 15 54 73 86 90 95 136 120 120 110 105 100 25.193 21.99 15.18 17.46 20.625 21.99 0.82 0.293 0.158 0.158 0.178 0.182 25 Formulae Used: Power (P) =  222 2 LRS IIIR  R = V / IR Power factor cos  = LR LRS II III 2 222  Model Calculations: Result: Thus power was measured using 3 ammeter method 26 Experiment No. 9 Date : CIRCUIT ANALYSIS USING CRO Aim: To measure voltage and current and also to study the phase relationship between supply voltage and current in series RC circuit. Apparatus Required: Sl.No. Apparatus Range Quantity 1 Function generator 1 2 DMM 1 3 Resistor 200  1 4 Capacitor 1 F 1 5 CRO 1 Procedure: 1. Connections are given as per the circuit diagram. 2. In the function generator, select “SINE WAVE” as the output and set the frequency to 200 Hz. 3. Adjust the amplitude knob of the function generator until the waveform on the oscilloscope shows 2 Vp. 4. Record the peak voltage across the resistor using CRO. 5. Calculate  from t. 6. Draw the waveform for VS, VR. Circuit Diagram: 27 Sl.No. Frequency (Hz) VR V T (ms) t (ms)  deg 1 200 0.4 5 0.3 21.6 (leading Sl.No. Frequency (Hz) VR V T (ms) t (ms)  deg 1 0.32 1.6mA 1.2 750 7.95 Result: The phase relationship between supply voltage and current in series RC circuit is studied and also the voltage and current are increased practically.