Lab E1 RLC Circuit 1

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Lab : E1 RLC Circuits

OBJECTIVE

The main objective of this experiment is to explain the working principle of an

alternating current (AC) in series and parallel configuration of the RLC circuits.

INTRODUCTION

In general, the RLC circuit is just is what the name is. Meaning the RLC circuit will

contain resistor, inductor and as well as a capacitor. When these 3 components areconnected in either series or parallel configuration, we can observe the differences.

(A)CapacitorA capacitor is a component which it does not allowed sudden change in voltage

in a circuit. In other words, it resists the changes of voltages. The capacitor is also

said that it can store charges as current flow through it. The phasor angle

between the voltage and current is 90.

(B)InductorAn inductor is a component which it does not allowed the sudden change in

current within a circuit. In other meaning, the inductor resist the changes occur

in the direction of the current flow. The inductor is also said that it can store

magnetic flux. The phasor angle between the current and voltage is 90 also.

(C)Reactance of the circuitBecause of the input is an alternating current (AC) power supply, thus there will

be frequency and we should take it into consideration when we do the

calculation. For inductors and capacitors, its reactance can be calculated by using

formula. The formula are given as below,

XC =1

C


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XL =L where, =2f

This can ease us in the calculating because with the reactance we had, we are

able to calculate the voltage as well as the current across the inductor and

capacitor and also the resistor in the RLC circuit no matter it is in the series orparallel configuration.

EQUIPMENTS

Connecting cables, digital multi-meter, oscilloscope, signal generator, bread board,

resistors (150, 200, 680 and 1k), capacitor (47F) and inductor (1000H)

PROCEDURE

(A)Series RLC Circuit

Figure 1 : The series configuration of RLC Circuit (Adapted from

http://www.electronics-tutorials.ws/accircuits/series-circuit.html)

1. The circuit in the diagram is being constructed on a bread board correctly.2. The alternating current (AC) power supply is being set to 12Vpp, with

frequency of 1 kHz to the input, and is rectangular shape input. This setting

can be double confirmed by connecting the AC power supply to the

oscilloscopes as the oscilloscopes can show the peak value of the power


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supply along with it frequency and the shape of the input.

3. By using digital multi-meter, the values needed in the Table 1 are beingmeasured.

4. This experiment is being repeated by replacing the 150 resistors with 200.680 and 1 k resistors.

5. In order to measure the current across the component, the digitalmulti-meter must be in series with the component.

(B)Parallel RLC Circuit

Figure 2 : The parallel configuration of RLC Circuit (Adapted from

http://www.electronics-tutorials.ws/accircuits/parallel-circuit.html)

1. The circuit in the diagram is being constructed on a bread board correctly.2. The alternating current (AC) power supply is being set to 12Vpp, with

frequency of 1 kHz to the input, and is rectangular shape input. This settingcan be double confirmed by connecting the AC power supply to the

oscilloscopes as the oscilloscopes can show the peak value of the power

supply along with it frequency and the shape of the input.

3. By using digital multi-meter, the values needed in the Table 1 are beingmeasured.

4. This experiment is being repeated by replacing the 150 resistors with 200.680 and 1 k resistors.


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5. In order to measure the current across the component, the digitalmulti-meter must be in series with the component.

RESULTS

A. Series RLC CircuitTable 1 : The voltage and current readings for each of the components in series

RLC circuit

Resistors Components Voltage, V (V) Current, I (mA)

150 R 4.44 29.84C 0.086 29.84

L 0.566 29.84

L,C,R 5.01 29.84

200 R 4.83 24.27

C 0.069 24.27

L 0.454 24.27

L,C,R 5.29 24.27

680 R 5.87 8.79C 0.024 8.79L 0.156 8.79

L,C,R 6.03 8.79

1 k R 6.04 6.14C 0.016 6.14

L 0.108 6.14

L,C,R 6.16 6.14

(A)XC and XL values of the series circuitTable 2 : The values of XC and XL for series circuit.

XC XL

Given XC = L

= 2fL

= 2(1000)(1000)

= 6.28

Given XL =1

C

=1

2fC

=1

(2)(1000)(47)


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= 3.39

(B)Mathematically total up the values of voltages across each of the components.VTotal = V2 + (VL VC)2

Table 3 : The mathematical and measuring values of the V Total for each resistors in

series circuit

Resistors () (VT)measurement (V) (VT)mathematical (V) % of error (%)150 5.01 4.46 12.33

200 5.29 4.84 9.30

680 6.03 5.87 2..73

1000 6.16 6.04 1.99

(C)The impedance Z of each of the resistors in series circuit.Given

Theoretical impedance for series circuit, ZsTheoretical = R2 + (XL XC)2Experimental impedance, ZExperimental=g ,,u ,,

Table 4 : The value of the impedances in series circuit

Resistors Series

ZsTheoretical ZsExperimental

150 150.03 167.90200 200.02 217.96680 680.01 686.01

1000 1000.00 1003.26

B. Parallel RLC CircuitTable 5 : The voltage and current readings for each of the components in parallel


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RLC circuit

Resistors Components Voltage, V (V) Current, I (mA)

150 R 0.388 2.52

C 0.388 12.9

L 0.388 99.8

L,C,R 0.400 122.5

200 R 0.400 1.89

C 0.390 12.97

L 0.390 100.6

L,C,R 0.394 122.5

680 R 0.393 0.55C 0.392 13.05

L 0.392 102.3

L,C,R 0.402 122.7

1 k R 0.391 0.37C 0.391 13.03

L 0.391 102.7

L,C,R 0.403 122.7

(A)XC and XL values of the series circuitTable 6 : The values of X

Cand X

Lfor parallel circuit

XC XL

Given XC = L

= 2fL

= 2(1000)(1000)

= 6.28

Given XL =1

C

=1

2fC

=1

(2)(1000)(47)

= 3.39

(B)Mathematically total up the values of voltages across each of the components.ITotal = I2 + (IL IC)2

Table 7 : The mathematical and measuring values of the V Total for each resistors in


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parallel circuit

Resistors () (IT)measurement (mA) (IT)mathematical (mA) % of error (%)150 122.5 86.94 40.90

200 122.5 87.65 39.76

680 122.7 89.25 37.48

1000 122.7 89.67 36.83

(C)The impedance Z of each of the resistors in series circuit.Given,

Theoretical impedance for parallel circuit,1

p= 1

2 + ( 1

1

)2

Experimental impedance, ZExperimental=g ,,u ,,

Table 8 : The value of the impedances in parallel circuit

Resistors Parallel

ZsTheoretical ZsExperimental

150 7.36 3.27200 7.36 3.22680 7.37 3.28

1000 7.37 3.28

DISCUSSION

(A)Series RLC CircuitIn this RLC series circuit, we can find out that the XC and XL is equal to 3.39 and

6.28 respectively. Besides that, as we can see from the Table 3, we can see that

the VTotal which are calculated through the mathematical way are very close to

the measuring way. The percentage of error is just varied from 2 to 12 %. With

this range of percentage, we can assure that the experiment is in the right track

but with some little mistakes that causes the deviation of the values. For

impedance, the experimental value is slightly differences from the theoretical

values. This might because of the errors occurs during the experiment and its will


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be stated in the Part C of the discussion part. But in general, the readings are just

slightly deviates therefore the readings still can be said as accurate.

(B)Parallel RLC CircuitIn this RLC parallel circuit, we can see that the XC and XL is equal to the values in

the series circuit. Besides that, the experimental values of the ITotal is seem to be

large differ than the theoretical values if we observe it through the percentage of

error. But in this case, we should not forget the values are actually measuring in

terms of mili-ampere (mA). Thus, because of the actual readings is in the power

of -3, which is a very small values, thus the accuracy of the digital multi-meter

should be take into the consideration. For the impedance of this circuit, the

values are quite different, this indicates that there might be something had went

wrong or may be is because of some errors.

(C)Error and PrecautionIn this experiment, there are some error occurred. One of the examples will be

the difference in the actual resistance of the resistors with the theoretical

assumed values. This can be seen in the Table 9. Besides of this error, thecomponents used in this experiment, includes the power supply and the

oscilloscope, there must be internal resistance, r in the component. When we do

the calculations, in order to decrease the deviation, we should take into account

the internal resistance as its will affect the real values during the experiments.

Apart from this, the jumper used in the experiment is having small values of

resistance as well. The only thing we can do to counter this issue is to prevent the

over-using of jumper and use it as least as possible. In this experiment, the bread

board is connected to the power supply throughout the experiment. In this case,the temperature of the components in the breadboard is keeps on increasing.

This incident will affects the readings as there will be more heat loss as power for

each of the components. As to prevent this from happening, we should turn off

the power supply during the time that we no need the use of the input supply.

Table 9 : The theoretical and real values of the resistance for each resistors.


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Resistors Theoretical () Real ()150 150 147.6200 200 197.7680 680 667

1000

1000 984

(D)CharacteristicsThere are some characteristics for the series and parallel RLC circuit we can

discussed about. The first one will be about the leading and lagging situation. In

the series RLC circuit, the VL is leading the VC by 90 as shown in the Figure 3.

While for parallel RLC circuit, the IC is leading the IL by 90 as shown in Figure 4.

Figure 3 : The Phasor diagram of the series configuration of the RLC circuit.


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Figure 4 : The Phasor diagram of the parallel configuration of the RLC circuit.

Apart from that, for the series RCL circuit, the current across each component is the

same while the algebraic sum of the voltage of the components with its phasor angle

is the total voltage. In the mean time, for the parallel RCL circuit, the voltage across

each of the components are the same while the algebraic sum of the currents across

each components with its own phasor angle is equal to the total current.

CONCLUSION

As conclusion, the operating principle for series and parallel configuration of RCL

circuit is understands and the objective is achieved.

REFERENCES

1. http://www.electronics-tutorials.ws/accircuits/series-circuit.html(Accessed on 11.12.2012 10.00am)

2. http://www.electronics-tutorials.ws/accircuits/parallel-circuit.html
http://www.electronics-tutorials.ws/accircuits/series-circuit.htmlhttp://www.electronics-tutorials.ws/accircuits/series-circuit.htmlhttp://www.electronics-tutorials.ws/accircuits/parallel-circuit.htmlhttp://www.electronics-tutorials.ws/accircuits/parallel-circuit.htmlhttp://www.electronics-tutorials.ws/accircuits/parallel-circuit.htmlhttp://www.electronics-tutorials.ws/accircuits/series-circuit.html


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(Accessed on 11.12.2012 10.00am)

3. http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html#c1 (Accessed on 11.12.2012 10.00am)

4. Alexander, C.K., Sadiku, M.N.O.(2007). Circuits theorems. Fundamentals of Electric Circuits.3

rdEdition. McGraw Hill. Pages: 331-336.

5. C.R. John. Basic AC Circuits (Second Edition), 2000, Pages 369-393
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html#c1http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html#c1

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Lab E1 RLC Circuit 1