Experiment 2: laboratory activity for the electrical ciruits PDF

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Experiment No. 2Sinusoidal Alternating Voltage for a CapacitorValerio, Kyle Gabriel C. 1 , Valete III, Alfredo R. 2 , Verin, Miguel Angelo D. 3 [email protected] 1 , Valetealfredoiii@gmail 2 , miguelangeloverin23011@gmail 3Introduction:In the early 1740s, scientist Ewald Georg von Kleist observed...

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Experiment No. 2 Sinusoidal Alternating Voltage for a Capacitor Valerio, Kyle Gabriel C.1, Valete III, Alfredo R.2, Verin, Miguel Angelo D.3 [email protected], [email protected], [email protected]

Introduction:

In the early 1740s, scientist Ewald Georg von Kleist observed that the element mercury can retain charges after electrification [1]. In these early years, the term used for the device is condenser based on its function as coined by another scientist named Alessandro Volta [2]. The phenomena that Kleist discovered is the first known invention of the electrical component called capacitor, in which later improved [3]. A capacitor is an electrical component that functions as an energy storage [4]. In this modern time, a capacitor is widely used in almost every electrical device that is invented [5]. The most basic part of capacitor is the two parallel conductive plates, these plates were separated at a certain distance by an insulator [6]. The insulating materials that were used in a capacitor are called dielectric materials [7]. A dielectric material has the ability to be polarize when an electrical potential is applied in the circuit [8]. The most commonly used dielectric materials are air, glass, aluminum oxide, paper, and mica [9]. In a direct current application, the capacitor acts like a break in the circuit, as there is no movement of electrons between the two plates [10]. The capacitor charges up upon voltage application, as equal to the source, and discharge when the voltage is low [11].

Objective: 1. To investigate the behavior of a capacitor (current and voltage characteristics) when a sinusoidal AC voltage is applied. Materials: 1. Function generator (Mode: Sine; Amplitude: 1:1,20%; Frequency: 100Hz) 2. Oscilloscope (Channel A: 1V/div, Channel B: 500mV/div, Time base: 5ms/div, Mode: X/T, AC Trigger: Channel A / rising edge / pre-trigger 0%) 3. 100 Ω resistor 4. 1microFarad capacitor

Procedure: 1. Assemble the circuit as shown in figure 1.

Figure 1. Circuit diagram

2. Use the function generator as the source. Set the function generator as indicated above. 3. Measure the voltage and current using oscilloscope. 4. Measure the period difference and compute the phase angle difference using this formula: ∅ =

𝑃𝑒𝑟𝑖𝑜𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑃𝑒𝑟𝑖𝑜𝑑 𝑓𝑜𝑟 1 𝑐𝑦𝑐𝑙𝑒

∗ 360°

5. Record results in Table 1 6. Increase the frequency to 1 kHz of the function generator. And repeat Step 3 and 4 7. Record results in Table 1 8. Observe the phase displacement between the current and voltage. 9. Observe the relationship between the frequency and peak current.

Results and Discussion: Table 1 100Hz

1kHz

Voltage

1.982 V

1.672 V

Current

1.262 mA

10.589 mA

Phase Angle Difference (V & I)

90°

90°

The simulated circuit for 100 Hertz:

Figure 2.1. The voltage of the circuit as seen in the simulated circuit for 100 Hz

Figure 2.2. The current of the circuit as seen in the simulated circuit for 100 Hz

Figure 2.3. The period difference of the waveform for 100 Hz

Figure 2.4. The period for one cycle of the waveforms for 100 Hz

The simulated circuit for 1000 Hertz:

Figure 3.1. The voltage of the circuit as seen in the simulated circuit for 1000 Hz

Figure 3.2. The current of the circuit as seen in the simulated circuit for 1000 Hz

Figure 3.3. The period difference of the waveform for 1000 Hz

Figure 3.4. The period for one cycle of the waveforms for 1000 Hz

In this experiment, the behavior of the capacitor is observed when the alternating voltage is applied. There are two different frequencies that were experimented which are the 100 Hertz and 1 kilohertz, and a sinusoidal voltage from the source. The circuit in this experiment contains series connected components which are the 100-ohm resistor and 1 microfarad capacitor. The behavior of the capacitor is observed in the circuit in terms of voltage, current, and the phase shift between the two signals when a sinusoid alternating voltage from different frequencies is applied. The voltage across the capacitor is measured using the oscilloscope, and a waveform representing the voltage in sinusoid is recorded. The voltage value in the experiment is determined by getting the peak value of the voltage waveform. In 100 Hertz set-up, the voltage is measured to have 1.982 volts, as seen in Figure 2.1. And when the source is in 1 kilohertz, the voltage is 1.672 volts, which is shown in Figure 3.1. It can be observed that the output voltage at lower frequency is higher than that with a high frequency from the source. The voltage across the capacitor is nearly the same with the source when the frequency is low [12]. But when the frequency is getting higher, the voltage value decreases significantly [13]. This is because the voltage drop developed in the resistor is much lower in comparison with the voltage potential across the capacitor, when the frequency from the source is low [14]. Simply, the output voltage across the capacitor is unaffected, producing nearly similar input and output voltage, in the application of very low input frequency, vice-versa [15]. Flow of electrons in the capacitor is also observed in this experiment. The oscilloscope is used to identify the output current waveform of the circuit. The peak value of the waveform that is produced represents the current of the circuit. In Figure 2.2, at 100 Hertz frequency input, the current is measured to have 1.262 milliamperes. On the other hand, the current in the 1 kilohertz input frequency have a value of 10.589 milliamperes, as observed in Figure 3.2. From those details, we can say that the current in the circuit increases as the value of the frequency increases [16]. The current value and input frequency are directly proportional with each other in this type of circuit. The quick changes in the rate of the voltage in the capacitor plates causes the increase in the flow of current when the frequency of the source is increased [17]. Meanwhile, the phase angle difference or phase shift between the voltage and current waveforms is being computed. The two quantities which are the period of one complete cycle and the time between the two waveforms at the zero transition are the vitals in determining the phase shift. The period for one complete cycle of the voltage waveform is determined for both frequencies. It is noticeable, as shown in Figure 2.4 and Figure 3.4, that the time it takes for a

wave to complete a cycle is larger in small frequency value, while higher frequency took only short time to complete one cycle [18]. The measured time in 100 Hertz frequency is 10 milliseconds while in the 1 kilohertz frequency, it only takes 1 millisecond to complete a cycle. On the other hand, the period difference is measured between the voltage and current waveforms. In Figure 2.3 it is measured that the 100 Hertz set-up have a period difference of 2.5 milliseconds, but the 1 kilohertz input has a difference value of 250 microseconds as seen in Figure 3.3. This time the high frequency input, 1 kilohertz, have smaller period difference in comparison with the small frequency input of 100 Hertz [19]. It can be noticed from the waveforms of the outputs that when the voltage is at its peak, the current is momentarily zero. And when the current is at its peak, the voltage is seen to be zero. This is because when voltage is suddenly applied, the charges build up in the capacitor plates making a zero-current flow in that certain region [20]. The phase shift or phase angle difference, in degrees, is then determined by dividing the period for one cycle and the period difference, and multiplying the quotient by 360 degrees. After mathematical computation, it is determined that both of the frequency has a phase shift of 90 degrees or

1 4

cycle between the two signals [21]. With this sense, it can be said that in a purely

capacitive circuit, there exist a 90 degrees phase difference or timing difference between the two waveforms or signals [22]. It can be observed in the two waveforms from the oscilloscope device that the current reached its maximum or peak value before the voltage reached its own peak. Based on the output waveforms, it is shown that in a purely capacitive circuit, the current leads the voltage by an angle of 90 degrees or one-fourth of a cycle [23].

Conclusion In this experiment, the behavior of a component which is the capacitor is observed through a series of simulation. Two frequencies were used for the input of the sinusoidal alternating voltage which are the 100 Hertz and the 1 kilohertz. The voltage across the capacitor varies with respect to the frequency of the input. The voltage in a purely capacitive circuit has an inverse relationship with the input frequency. Higher frequency from the source will result to a smaller voltage value across the capacitor. While having a low frequency input will produce an output that is nearly the same of the input voltage source. The voltage drop across the capacitor is much lower compared to the electric potential across the resistor at high frequencies. Current in this type of circuit also changes with respect to the input frequency. The current or flow of electrons in the circuit is high in value when the input frequency is also high. And when frequency is low, the current that is flowing is less. This phenomenon is due to the fact that there is a small rate of change in voltage from the parallel conductive plates of the capacitor when there is a low frequency input, thus having less current flow. Otherwise, high frequency in the input means the voltage change rate in the capacitor plates is faster, which results to greater current flow. In short, the peak current in the capacitive ac circuit is in direct proportionality with the frequency of the input source. In a purely capacitive circuit, the charges initially build up in the capacitor plates when alternating sinusoidal voltage is suddenly applied, making no current flow. This is evidently seen in the two waveforms or signals wherein when the voltage is at its peak, the current is in zero line. Similarly, when the peak current is reached, the voltage is the one that is in zero line. In this circuit, it is evidently seen through the output waveforms that there is a difference in the phase between the voltage and current. It suggests that the voltage lags the current by a certain degree angle. This idea is applied to a capacitive circuit, in any input frequency. The phase shift between the voltage and current is determined by getting the ratio of the period difference and the period for one cycle. The period for one cycle and the period difference between voltage and current signals are high at low frequency. This change is in a constant ratio when examined in a purely capacitive circuit, which has a difference of

1 4

cycle. This is the reason

why the phase angle difference is the same despite of change in frequency. The phase angle difference for both frequencies is exactly similar. In a purely capacitive circuit, the peak current is reached 90 degrees or

1 4

cycle before the peak voltage is reached when a sinusoidal alternating

voltage is supplied from the source. The phase shift will be 90 degrees or one-fourth cycle even there is a change in frequency from the source. The circuit that is experimented is commonly applied in low frequency applications such as a low pass filter circuit. This circuit filters the unwanted signals, it allows the low frequency signals and blocking the high ones. This is very useful in circuit designs that requires a particular value of electrical signals. The devices such as audio amplifiers and speaker systems used this filter to direct frequencies and produce an efficient and effective output.

References

[1]

The Editors of Encyclopedia Britannica, “Capacitance,” Encyclopedia Britannica. 20-Nov2019.

[2]

S. Dufresne, “History of the capacitor – the pioneering years,” Hackaday.com, 12-Jul2016. [Online]. Available: https://hackaday.com/2016/07/12/history-of-the-capacitor-thepioneering-years/. [Accessed: 01-Jun-2021].

[3]

“Capacitors,” Ethw.org. [Online]. Available: https://ethw.org/Capacitors. [Accessed: 01Jun-2021].

[4]

C. Cunningham, “Circuit playground: C is for Capacitor,” Adafruit.com, 09-May-2014. [Online]. Available: https://learn.adafruit.com/circuit-playground-c-is-for-capacitor/what-isa-capacitor. [Accessed: 01-Jun-2021].

[5]

“How do capacitors work?,” Explainthatstuff.com, 16-Aug-2008. [Online]. Available: https://www.explainthatstuff.com/capacitors.html. [Accessed: 01-Jun-2021].

[6]

Electronics-tutorials.ws. [Online]. Available: https://www.electronicstutorials.ws/capacitor/cap_1.html. [Accessed: 01-Jun-2021].

[7]

Boundless, “Capacitors and Dielectrics,” Lumenlearning.com. [Online]. Available: https://courses.lumenlearning.com/boundless-physics/chapter/capacitors-and-dielectrics/. [Accessed: 01-Jun-2021].

[8]

“Dielectrics article (article),” Khanacademy.org. [Online]. Available: https://www.khanacademy.org/science/in-in-class-12th-physics-india/in-in-electrostaticpotential-and-capacitance/x51bd77206da864f3:effect-of-dielectric-oncapacitance/a/dielectric-article. [Accessed: 01-Jun-2021].

[9]

“The dielectric constant and its effects on the properties of a capacitor,” Passivecomponents.eu, 15-Nov-2017. [Online]. Available: https://passive-components.eu/thedielectric-constant-and-its-effects-on-the-properties-of-a-capacitor/. [Accessed: 01-Jun2021].

[10] Utexas.edu. [Online]. Available: http://farside.ph.utexas.edu/teaching/302l/lectures/node60.html. [Accessed: 01-Jun-2021]. [11] G. Patil, “How capacitor works with DC,” Binaryupdates.com, 14-Mar-2017. [Online]. Available: https://binaryupdates.com/how-capacitor-works-with-dc/. [Accessed: 20-Jun2021]. [12] Electronics-tutorials.ws. [Online]. Available: https://www.electronicstutorials.ws/filter/filter_2.html. [Accessed: 20-Jun-2021].

[13] Administrator, “First order and second order passive Low Pass filter circuits,” Electronicshub.org, 17-Jan-2019. [Online]. Available: https://www.electronicshub.org/passive-low-pass-rc-filters/. [Accessed: 20-Jun-2021]. [14] “Passive Low Pass Filter,” Circuitdigest.com, 12-Feb-2018. [Online]. Available: https://circuitdigest.com/tutorial/passive-low-pass-filter. [Accessed: 20-Jun-2021]. [15] “No title,” Physics.bu.edu. [Online]. Available: http://physics.bu.edu/~duffy/semester2/d21_filters.html. [Accessed: 20-Jun-2021]. [16] Electronics-tutorials.ws. [Online]. Available: https://www.electronicstutorials.ws/accircuits/ac-capacitance.html. [Accessed: 20-Jun-2021]. [17] Electronics-tutorials.ws. [Online]. Available: https://www.electronicstutorials.ws/filter/filter_1.html. [Accessed: 20-Jun-2021]. [18] “13.2 wave properties: Speed, amplitude, frequency, and period,” Openstax.org. [Online]. Available: https://openstax.org/books/physics/pages/13-2-wave-properties-speedamplitude-frequency-and-period. [Accessed: 20-Jun-2021]. [19] Allaboutcircuits.com. [Online]. Available: https://www.allaboutcircuits.com/textbook/alternating-current/chpt-4/ac-capacitor-circuits/. [Accessed: 20-Jun-2021]. [20] Physics.bu.edu. [Online]. Available: http://physics.bu.edu/~duffy/PY106/ACcircuits.html. [Accessed: 20-Jun-2021]. [21] “Phase Shift,” Gov.mo. [Online]. Available: http://www.cmm.gov.mo/eng/exhibition/secondfloor/MoreInfo/2_4_4_PhaseShift.html. [Accessed: 20-Jun-2021]. [22] “Phase Shift,” Learnabout-electronics.org. [Online]. Available: https://learnaboutelectronics.org/ac_theory/ac_ccts_51.php. [Accessed: 20-Jun-2021]. [23] “Phase Relationships in AC Circuits,” Gsu.edu. [Online]. Available: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/phase.html. [Accessed: 20-Jun-2021].

APPENDICES APPENDIX A: THEORETICAL COMPUTATIONS 1. The phase angle of the circuit having the frequency of 100 Hertz ∅=

𝑃𝑒𝑟𝑖𝑜𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 ∗ 360° 𝑃𝑒𝑟𝑖𝑜𝑑 𝑓𝑜𝑟 1 𝑐𝑦𝑐𝑙𝑒

∅=

2.5 × 10−3 ∗ 360° 10 × 10−3 ∅ = 90°

2. The phase angle difference of the circuit having the frequency of 1000 Hertz ∅=

𝑃𝑒𝑟𝑖𝑜𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑃𝑒𝑟𝑖𝑜𝑑 𝑓𝑜𝑟 1 𝑐𝑦𝑐𝑙𝑒

∅=

∗ 360°

250 × 10−6 ∗ 360° 1 × 10−3 ∅ = 90°

APPENDIX B: MEETING OF THE GROUP WHILE WORKING WITH THE EXPERIMENT (PICTURE- VIRTUAL MEETING)...