lab e1 rlc circuit

Yong Ching Wai KEU110049 Lab E1 RCL Circuits

DEPARTMENT OF BIOMEDICAL ENGINEERING

FACULTY OF ENGINEERING

UNIVERSITY MALAYA

Lab : E1 RLC Circuits

Name : Yong ChingWai

Date : 06.11.2012

Course Code :KUEU 2173 LABORATORY PRACTICAL 3

Matrix Number : KEU110049

Lab Lecturer’s Name : Dr. Muhammad Shamsul arefeen

Zilany

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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 are connected in either series or parallel configuration, we can observe the differences.

(A) Capacitor

A 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) Inductor

An 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 circuit

Because 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 = 1ωC

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XL =ωL where, ω=2πf

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 or parallel configuration.

EQUIPMENTS

Connecting cables, digital multi-meter, oscilloscope, signal generator, bread board, resistors (150Ω, 200Ω, 680Ω and 1kΩ), capacitor (47μF) and inductor (1000μH)

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 being measured.

4. This experiment is being repeated by replacing the 150Ω resistors with 200Ω. 680Ω and 1 kΩ resistors.

5. In order to measure the current across the component, the digital multi-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 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 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 being measured.

4. This experiment is being repeated by replacing the 150Ω resistors with 200Ω.

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680Ω and 1 kΩ resistors.

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

RESULTS

A. Series RLC Circuit

Table 1 : The voltage and current readings for each of the components in series RLC circuit

Resistors Components Voltage, V (V) Current, I (mA)150Ω R 4.44 29.84

C 0.086 29.84L 0.566 29.84

L,C,R 5.01 29.84200Ω R 4.83 24.27

C 0.069 24.27L 0.454 24.27

L,C,R 5.29 24.27680Ω R 5.87 8.79

C 0.024 8.79L 0.156 8.79

L,C,R 6.03 8.791 kΩ R 6.04 6.14

C 0.016 6.14L 0.108 6.14

L,C,R 6.16 6.14

(A) XC and XL values of the series circuit

Table 2 : The values of XC and XL for series circuit.

XC XL

Given XC = ωL = 2πfL = 2π(1000)(1000μ)

Given XL = 1ωC

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= 6.28 Ω = 12π fC

= 1

(2π ) (1000 )(47μ) = 3.39 Ω

(B) Mathematically total up the values of voltages across each of the components.

VTotal = √V R2+(V L−V C )2

Table 3 : The mathematical and measuring values of the VTotal for each resistors in series circuit

Resistors (Ω) (VT)measurement (V) (VT)mathematical (V) % of error (%)150 5.01 4.46 12.33200 5.29 4.84 9.30680 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+(X L−XC )2

Experimental impedance, ZExperimental= Voltage across components L ,C , R

Current across componentsL, C , R

Table 4 : The value of the impedances in series circuit

Resistors SeriesZsTheoretical ZsExperimental

150Ω 150.03 167.90200Ω 200.02 217.96680Ω 680.01 686.01

1000Ω 1000.00 1003.26

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B. Parallel RLC Circuit

Table 5 : The voltage and current readings for each of the components in parallel RLC circuit

Resistors Components Voltage, V (V) Current, I (mA)150Ω R 0.388 2.52

C 0.388 12.9L 0.388 99.8

L,C,R 0.400 122.5200Ω R 0.400 1.89

C 0.390 12.97L 0.390 100.6

L,C,R 0.394 122.5680Ω R 0.393 0.55

C 0.392 13.05L 0.392 102.3

L,C,R 0.402 122.71 kΩ R 0.391 0.37

C 0.391 13.03L 0.391 102.7

L,C,R 0.403 122.7

(A) XC and XL values of the series circuit

Table 6 : The values of XC and XL for parallel circuit

XC XL

Given XC = ωL = 2πfL = 2π(1000)(1000μ) = 6.28 Ω

Given XL = 1ωC

= 12π fC

= 1

(2π ) (1000 )(47μ) = 3.39 Ω

(B) Mathematically total up the values of voltages across each of the components.

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ITotal = √ IR2+( I L−IC )2

Table 7 : The mathematical and measuring values of the VTotal for each resistors in parallel circuit

Resistors (Ω) (IT)measurement (mA) (IT)mathematical (mA) % of error (%)150 122.5 86.94 40.90200 122.5 87.65 39.76680 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, 1ZpTheoretical

= √ 1R 2+( 1X L

− 1XC

)2

Experimental impedance, ZExperimental= Voltage across components L ,C , R

Current across componentsL, C , R

Table 8 : The value of the impedances in parallel circuit

Resistors ParallelZsTheoretical ZsExperimental

150Ω 7.36 3.27200Ω 7.36 3.22680Ω 7.37 3.28

1000Ω 7.37 3.28

DISCUSSION

(A) Series RLC Circuit

In this RLC series circuit, we can find out that the XC and XL is equal to 3.39Ω and 6.28Ω respectively. Besides that, as we can see from the Table 3, we can see that

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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 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 Circuit

In 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 Precaution

In 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, the components 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

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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.

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

1000Ω 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

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

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


(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.

3rd Edition. McGraw Hill. Pages: 331-336.

5. C.R. John. Basic AC Circuits (Second Edition), 2000, Pages 369-393

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http://hyperphysics.phy-astr.gsu.edu/hbase/electric/rlcser.html#c1

lab e1 rlc circuit

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