(EEE230)

EXPERIMENT 4

THEVENIN’S THEOREM AND WHEATSTONE BRIDGE

OBJECTIVES

1. To analyze DC resistive circuits using Thevenin’s Theorem.

2. To analyze an unbalanced Wheatstone bridge using Thevenin’s Theorem.

LIST OF REQUIREMENTS

Equipments

1. DC power supply.

2. Galvanometer.

3. Digital multimeter.

4. Analogue multimeter.

Components

1. Resistor: 2.2kΩ, 1.2kΩ, 10kΩ, 3.3kΩ

2. Decade resistance.

THEORY

INTRODUCTION

In 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 using

Thevenin’s Theorem. Lastly, we have learned how to calculate the value of V TH and RTH using

Thevenin’s Theorem.

THEVENIN’S THEOREM

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Thevenin’s Theorem states that a linear two-terminal circuit can be replaced by an equivalent

circuit consisting of a voltage source V TH in series with a resistor RTH , where V TH is the open-

circuit voltage at the terminals and RTH is the input or equivalent resistance at the terminals

when the independent sources are turned off.

Steps On Calculating V TH, RTH and IR

Figure 4.1 : Thevenin Equivalent Voltage (V TH )

V TH or Thevenin Equivalent Voltage is the value of voltage from point ‘a’ and point ‘b’. Note that

no current flows through R2, so there is no voltage drop across R2. To calculate the value, we

can use the equation 1.1.

V TH=VR3

R3+R4(Equation 1.1)

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Figure 4.2 : Thevenin Equivalent Resistance (RTH )

RTH or Thevenin Equivalent Resistance value can be found by calculating the value using the

equation 1.2.

RTH=R3 R4R3+R4

+R2(equation 1.2)

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Figure 4.3

To find IR, first we have to reattach R between to ‘a’ and ‘b’, put RTH in series with R and place

V TH on the circuit as in Figure 4.3. Then calculate the current through R using the equation 1.3.

IR=V THRTH+R

(equation 1.3)

To find voltage across R, use this equation 1.4.

V R=IR=V TH R

RTH+R(equation 1.4)

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WHEATSTONE BRIDGE

The 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 a

diamond pattern.

A DC voltage is connected across two opposite points of the diamond, and a

galvanometer is bridged across the other two points. When all four of the resistances bear a

fixed relationship to each other, the currents flowing through the two arms of the circuit will be

equal, and no current will flow through the galvanometer. By varying the value of one of the

known 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 unknown

electrical resistance by balancing the resistances in the two branches of a bridge circuit, one

branch of which includes the unknown resistance.

Figure 4.4

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In the circuit shown in Figure 4.4, let R1 be the unknown resistance and R2, R3 and R4

are resistances of known value and the resistance of R3 is adjustable. If the ratio of the two

resistances in the lower branch ¿¿¿ is equal to the ratio of the two unknown legs ¿¿¿, then the

output voltage (V o) between the two midpoints will be zero and no current will flow between the

midpoints. R3 is varied until this condition is reached. Then,

R1=R3¿¿¿

If V i is the impressed voltage, then current i1=V i /(R1+R2) and i2=V i /(R3+R4)

Voltage at A, V A=V i−R1×i1

Voltage at B, V B=V i−R3×i2

Now to have the voltage difference between A & B to be zero, V AB = 0

VA = VB

Detecting zero current can be done to extremely high accuracy. Therefore, if R2, R3 and

R4 are known to high precision, then R1 can be measured to high precision. Very small changes

in R1 disrupt the balance and are readily detected.

Alternatively, if R2, R3 and R4 are known, but R3 is not adjustable, and the impressed

voltage (V ¿¿ i)¿is known, then the voltage or current flow through the midpoints can be used to

calculate value of R1. This setup is frequently used in strain gauge measurements, as it is

usually faster to read a voltage level off a meter than to adjust a resistance to zero the voltage.

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PROCEDURES

PART A: THEVENIN’S THEOREM

Figure 4.8

Figure 4.9 (a) and (b)

Figure 4.10

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1. The circuit in Figure 4.8 was connected.

2. The current through R3 (I ¿¿R3)¿ and the voltage across R3 (V ¿¿ R3)¿ was

measured. The results was recorded in Table 4.1 (without using Thevenin’s Theorem).

3. R3 was removed and was connected in the circuit as in Figure 4.9(a) (Figure 4.8 with

R3 removed). The voltage across point ‘a’ and ‘b’ was measured and recorded it as V TH

.

4. The cirdcuit was construct as in Figure 4.9(b) (Figure 4.8 with R3 removed and the 12 V

source replaced by a short circuit). The resistance at point ‘a’ and ‘b’ was measured and

recorded it as RTH .

5. The circuit was constructed as in Figure 4.10. A resistor for RTH was obtained as close

as possible to its value using decade box.

6. The current through R3 and the voltage across R3 in the circuit of Figure 4.10 was

measured. The result was recorded in Table 4.1.

7. The percent of error between V TH (estimated) was calculated from theory with V TH from

step 3.

8. The percent of error between RTH (estimated) was calculated from theory with RTH from

step 4.

9. The percent of error between IR3 (estimated) was calculated from theory with IR3 using

Thevenin’s Theorem and without using Thevenin’s Theorem.

10. The percent of error between V R3 (estimated) was calculated from theory with V R3

using Thevenin’s Theorem and without using Thevenin’s Theorem.

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PART B: WHEATSTONE BRIDGE

Figure 4.11

Figure 4.12

Refer to Figure 4.11, set R1 = 2.3 kΩ (use decade resistance) and R2 = R3 = R4 = 2.2kΩ.

1. The internal resistance of the galvanometer, RG was measured.

2. The circuit was constructed as in Figure 4.11 and the galvanometer current, IG was

measured.

3. The galvanometer was removed from the circuit and V TH was measured The equivalent

circuit was modified and RTH was measured.

4. IG was calculated when the galvanometer is connected to the equivalent Thevenin

circuit (from step 3) as shown in Figure 4.12.

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5. The percent of error between IG (estimated) was calculated from theory and from step

2.

6. The percent of error between IG (estimated) was calculated from theory and calculated

IG from step 4.

7. The the percent of error between V TH (estimated) was calculated from theory with V TH

from step 3.

8. The the percent of error between RTH (estimated) was calculated from theory with RTH

from step 3.

9. Step 1 to 8 for R1 = 2.0 kΩ and 2.5kΩ was repeated and the results was recorded in

Table 4.2.

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RESULTS

a)Thevenin’s Theorem

QuantityEstimated Value

(Pre-Lab)

Measured Value

Without Using

Thevenin’s Theorem

Using Thevenin’s

Theorem

V TH 10.71 V - 11.05 V

RTH 1.071 kΩ - 1.074 kΩ

Current through R3(I ¿¿R3)¿2.45 mA 2.40 mA 2.40 mA

Voltage through R3(V ¿¿ R3)¿8.08 V 8.00 V 8.30 V

Table 4.1

b)Wheatstone Bridge

R1 2.3kΩ 2.0kΩ 2.5kΩ

RG 21.5 Ω 21.5 Ω 21.5 Ω

V TH (estimated ) 0.11 V -0.24 V 0.319 V

RTH (estimated ) 2.22 kΩ 2.15 kΩ 2.27 kΩ

IG(estimated ) 49.46µA -110.8 µA 140.5µA

IG(step2) 36 µA -90µA 120µA

V TH (step3) 0.13 V -0.23V 0.34V

RTH (step3) 2.2 kΩ 2.1 kΩ 2.3 kΩ

% of error IG(step5) 27.2% 18.8% 14.6%

% of error V TH (step7) 17.3% 5.0% 7.2%

% of errorRTH (step8) 0.9% 1.4% 0.9%

Table 4.2

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Discussion

For part A, Thevenin’s Theorem states that in order for us to find the current flows

through a resistor R which connected across any two points ‘a’ and ‘b’ of an active network is by

dividing the potential difference between ‘a’ and ‘b’ (with R disconnected) by R+r, where r is the

resistance of the network measured between ‘a’ and ‘b’ when R disconnected and the sources

of E.M.F has been replaced by their values of internal resistance.

The value of V TH and RTH need to be measured using Thevenin Theorem since the

resistor R was disconnected from the circuit.So there are no current flows through resistor R2

.and no voltage drop at R2.

From the result,The value of V TH and RTH expected is slightly different from the

measured value and The value for V R3 and IR3 without using and using Thevenin’s Theorem

and the expected values are also different because while conducting this experiment ,there

might have some errors.Maybe this error occur because we using connecting wires.In

connecting wires it have some resistance values so it will affect our final values.From the table

4.1,the value V R3 with using Thevenin’s Theorem are a bit higher than without using Thevenin’s

Theorem .It can show us that connecting wires have resistance values since we use more

connecting wires when want measure V R3 without using Thevenin’s theorem than using

thevenin’s theorem circuit.

Based on the Table 4.2 ,We can see that galvanometer has internal resistance.That

means it can affect our final measured Values.The Values of VTH,RTH and IG estimate is

different with measured values.As in experiment part A.The connecting wires has resistance

values 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 some

error while connecting the circuit as the example the decade resistor box maybe have some

internal resistance that affect our values.While the RTH the error is not too high .As in this

experiment we was using Analogue multimeter to measure VTH an IG so the parallax error can

be occurs since our eyes sometimes does not perpendicular toward the scale of analogue

meter.So we need make sure the scale is perpendicular toward our eyes.

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To Measure RTH by using Thevenin’s Theorem we need to make sure all DC voltage is

removed from the circuit or short circuit.It is because we need pure of resistance since when

voltage flow on the resistance it will affect the reading of RTH. To measure VTH and IG we can

just put the measure probe to point “c” and “d” as in Figure 4.11 without change the original

condition of the loads in the circuit.

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CONCLUSION

After doing the experiment, we can conclude that by using Thevenin’s Theorem, we can

analyze DC resistive circuit and analyze an unbalanced Wheatstone bridge circuit. We also

know that without using Thevenin’s Theorem, we could not find V TH , RTH, IR and V R in a very

complex circuit .Thevenin’s Theorem is very important in circuit analysis. It helps us to simplify a

large circuit by replacing the circuit into a single independent source and a single resistor. This

replacement technique is very useful in circuit design.This lab is also effectively showed how the

Wheatstone bridge provides a mechanism to calculate an unknown resistance using the known

relationships given through the resistivity correlation to length. It demonstrated how to set-up a

Wheatstone bridge and how to construct a Wheatstone bridge in a laboratory setting.As in this

experiment we can measure the V TH, RTH, and IG by using Thevenin’s theorem.We can

measure IG and VTH by connecting the measure probe to complete circuit but for RTH we need to

make sure no DC voltage flows in the circuit to follow the Thevenin’s Theorem rules.

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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

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