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- 1. (EEE230) EXPERIMENT 4 THEVENIN’S THEOREM AND WHEATSTONE BRIDGEOBJECTIVES 1. To analyze DC resistive circuits using Thevenin‟s Theorem. 2. To analyze an unbalanced Wheatstone bridge using Thevenin‟s Theorem.LIST OF REQUIREMENTSEquipments 1. DC power supply. 2. Galvanometer. 3. Digital multimeter. 4. Analogue multimeter.
- 2. Components 1. Resistor: 2.2kΩ, 1.2kΩ, 10kΩ, 3.3kΩ 2. Decade resistance.THEORYINTRODUCTIONIn this experiment, we have learned about the Thevenin‟s Theorem and Wheatstone bridge.Firstly, we have learned how to analyze DC resistive circuits using Thevenin‟s Theorem.Secondly, we also have learned how to analyze an unbalanced Wheatstone bridge usingThevenin‟s Theorem. Lastly, we have learned how to calculate the value of and usingThevenin‟s Theorem.THEVENIN’S THEOREM 1
- 3. Thevenin‟s Theorem states that a linear two-terminal circuit can be replaced by an equivalentcircuit consisting of a voltage source in series with a resistor , where is the open-circuit voltage at the terminals and is the input or equivalent resistance at the terminalswhen the independent sources are turned off.Steps On Calculating , and Figure 4.1 : Thevenin Equivalent Voltage or Thevenin Equivalent Voltage is the value of voltage from point „a‟ and point „b‟. Note thatno current flows through , so there is no voltage drop across . To calculate the value, wecan use the equation 1.1. (Equation 1.1) 2
- 4. Figure 4.2 : Thevenin Equivalent Resistance or Thevenin Equivalent Resistance value can be found by calculating the value using theequation 1.2. (equation 1.2) 3
- 5. Figure 4.3To find , first we have to reattach R between to „a‟ and „b‟, put in series with R and place on the circuit as in Figure 4.3. Then calculate the current through R using the equation 1.3. (equation 1.3)To find voltage across R, use this equation 1.4. (equation 1.4) 4
- 6. WHEATSTONE BRIDGEThe most accurate measurements of resistance are made with a galvanometer (or a voltmeter)in a circuit called a Wheatstone bridge, named after the British physicist Charles Wheatstone.This circuit consists of three known resistances and an unknown resistance connected in adiamond pattern. A DC voltage is connected across two opposite points of the diamond, and agalvanometer is bridged across the other two points. When all four of the resistances bear afixed relationship to each other, the currents flowing through the two arms of the circuit will beequal, and no current will flow through the galvanometer. By varying the value of one of theknown resistances, the bridge can be made to balance for any value of unknown resistance,which can then be calculated from the values of the other resistors. A Wheatstone bridge is a measuring instrument which is used to measure an unknownelectrical resistance by balancing the resistances in the two branches of a bridge circuit, onebranch of which includes the unknown resistance. Figure 4.4 5
- 7. In the circuit shown in Figure 4.4, let be the unknown resistance and , andare resistances of known value and the resistance of is adjustable. If the ratio of the tworesistances in the lower branch is equal to the ratio of the two unknown legs ,then the output voltage between the two midpoints will be zero and no current will flowbetween the midpoints. is varied until this condition is reached. Then,If is the impressed voltage, then current andVoltage at A,Voltage at B,Now to have the voltage difference between A & B to be zero, =0 VA = VB Detecting zero current can be done to extremely high accuracy. Therefore, if , and are known to high precision, then can be measured to high precision. Very small changesin disrupt the balance and are readily detected. Alternatively, if , and are known, but is not adjustable, and the impressedvoltage is known, then the voltage or current flow through the midpoints can be used tocalculate value of . This setup is frequently used in strain gauge measurements, as it isusually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage. 6
- 8. PROCEDURESPART A: THEVENIN’S THEOREM Figure 4.8 Figure 4.9 (a) and (b) Figure 4.10 7
- 9. 1. The circuit in Figure 4.8 was connected.2. The current through and the voltage across was measured. The results was recorded in Table 4.1 (without using Thevenin‟s Theorem).3. was removed and was connected in the circuit as in Figure 4.9(a) (Figure 4.8 with removed). The voltage across point „a‟ and „b‟ was measured and recorded it as .4. The cirdcuit was construct as in Figure 4.9(b) (Figure 4.8 with removed and the 12 V source replaced by a short circuit). The resistance at point „a‟ and „b‟ was measured and recorded it as .5. The circuit was constructed as in Figure 4.10. A resistor for was obtained as close as possible to its value using decade box.6. The current through and the voltage across in the circuit of Figure 4.10 was measured. The result was recorded in Table 4.1.7. The percent of error between (estimated) was calculated from theory with from step 3.8. The percent of error between (estimated) was calculated from theory with from step 4.9. The percent of error between (estimated) was calculated from theory with using Thevenin‟s Theorem and without using Thevenin‟s Theorem.10. The percent of error between (estimated) was calculated from theory with using Thevenin‟s Theorem and without using Thevenin‟s Theorem. 8
- 10. PART B: WHEATSTONE BRIDGE Figure 4.11 Figure 4.12 Refer to Figure 4.11, set = 2.3 kΩ (use decade resistance) and = = = 2.2kΩ. 1. The internal resistance of the galvanometer, was measured. 2. The circuit was constructed as in Figure 4.11 and the galvanometer current, was measured. 3. The galvanometer was removed from the circuit and was measured The equivalent circuit was modified and was measured. 4. was calculated when the galvanometer is connected to the equivalent Thevenin circuit (from step 3) as shown in Figure 4.12. 5. The percent of error between (estimated) was calculated from theory and from step 2. 6. The percent of error between (estimated) was calculated from theory and calculated from step 4. 9
- 11. 7. The the percent of error between (estimated) was calculated from theory with from step 3.8. The the percent of error between (estimated) was calculated from theory with from step 3.9. Step 1 to 8 for = 2.0 kΩ and 2.5kΩ was repeated and the results was recorded in Table 4.2. 10
- 12. RESULTS a)Thevenin‟s Theorem Measured Value Estimated ValueQuantity Without Using Using Thevenin‟s (Pre-Lab) Thevenin‟s Theorem Theorem 10.71 V - 11.05 V 1.071 kΩ - 1.074 kΩ 2.45 mA 2.40 mA 2.40 mA 8.08 V 8.00 V 8.30 V Table 4.1 b)Wheatstone Bridge 2.3kΩ 2.0kΩ 2.5kΩ 21.5 Ω 21.5 Ω 21.5 Ω 0.11 V -0.24 V 0.319 V 2.22 kΩ 2.15 kΩ 2.27 kΩ 49.46µA -110.8 µA 140.5µA 36 µA -90µA 120µA 0.13 V -0.23V 0.34V 2.2 kΩ 2.1 kΩ 2.3 kΩ% of error 27.2% 18.8% 14.6%% of error 17.3% 5.0% 7.2%% of error 0.9% 1.4% 0.9% Table 4.2 11
- 13. Discussion For part A, Thevenin‟s Theorem states that in order for us to find the current flowsthrough a resistor R which connected across any two points „a‟ and „b‟ of an active network is bydividing the potential difference between „a‟ and „b‟ (with R disconnected) by R+r, where r is theresistance of the network measured between „a‟ and „b‟ when R disconnected and the sourcesof E.M.F has been replaced by their values of internal resistance. The value of and need to be measured using Thevenin Theorem since theresistor R was disconnected from the circuit.So there are no current flows through resistor .and no voltage drop at . From the result,The value of and expected is slightly different from themeasured value and The value for and without using and using Thevenin‟s Theorem andthe expected values are also different because while conducting this experiment ,there mighthave some errors.Maybe this error occur because we using connecting wires.In connectingwires it have some resistance values so it will affect our final values.From the table 4.1,the value with using Thevenin‟s Theorem are a bit higher than without using Thevenin‟s Theorem .Itcan show us that connecting wires have resistance values since we use more connecting wireswhen want measure without using Thevenin‟s theorem than using thevenin‟s theoremcircuit. Based on the Table 4.2 ,We can see that galvanometer has internal resistance.Thatmeans it can affect our final measured Values.The Values of VTH,RTH and IG estimate isdifferent with measured values.As in experiment part A.The connecting wires has resistancevalues that affect our measured Values.From the calculated percent error of VTH,RTH and IG,We can see the how big the error occur,For the VTH and IG the error is high because someerror while connecting the circuit as the example the decade resistor box maybe have someinternal resistance that affect our values.While the RTH the error is not too high .As in thisexperiment we was using Analogue multimeter to measure VTH an IG so the parallax error canbe occurs since our eyes sometimes does not perpendicular toward the scale of analoguemeter.So we need make sure the scale is perpendicular toward our eyes. 12
- 14. To Measure RTH by using Thevenin‟s Theorem we need to make sure all DC voltage isremoved from the circuit or short circuit.It is because we need pure of resistance since whenvoltage flow on the resistance it will affect the reading of RTH. To measure VTH and IG we canjust put the measure probe to point “c” and “d” as in Figure 4.11 without change the originalcondition of the loads in the circuit. 13
- 15. CONCLUSION After doing the experiment, we can conclude that by using Thevenin‟s Theorem, we cananalyze DC resistive circuit and analyze an unbalanced Wheatstone bridge circuit. We alsoknow that without using Thevenin‟s Theorem, we could not find , , and in a verycomplex circuit .Thevenin‟s Theorem is very important in circuit analysis. It helps us to simplify alarge circuit by replacing the circuit into a single independent source and a single resistor. Thisreplacement technique is very useful in circuit design.This lab is also effectively showed how theWheatstone bridge provides a mechanism to calculate an unknown resistance using the knownrelationships given through the resistivity correlation to length. It demonstrated how to set-up aWheatstone bridge and how to construct a Wheatstone bridge in a laboratory setting.As in thisexperiment we can measure the , , and IG by using Thevenin‟s theorem.We canmeasure IG and VTH by connecting the measure probe to complete circuit but for RTH we need tomake sure no DC voltage flows in the circuit to follow the Thevenin‟s Theorem rules. 14
- 16. REFERENCES 1. Alexander, C.K., & Sadiku, M.N.O. (2004). Fundamentals of Electric Circuits : Fourth Edition. New York: McGraw Hill. 2. http://www.megaessays.com 3. Rusnani Ariffin & Mohd Aminudin Murad (2011).Laboratory Manual Electrical Engineering Laboratory 1:University Publication Center (UPENA). 4. http://www.allaboutcircuits.com/vol_1/chpt_10/8.html 5. http://www.efunda.com/designstandards/sensors/methods/wheatstone_bridge.cfm 15

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