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LaboratoryReportonRCTimeConstantscorrection1.docx1
Laboratory Report on RC Time Constants
Student’s Name
Professor’s Name
Course Name
Date
Abstract:
A resistor-capacitor (RC) circuit or RC line or RC organization is an electrical circuit consisting of a resistor and a capacitor. These can be driven very well by voltage or current sources, and they will produce different responses. This experiment seeks to examine how RC circuits can be used to transmit signals by jamming at certain frequencies and across other frequencies. RC circuits can be used to transmit signals by jamming at certain frequencies and across other frequencies. The two most normal RC channels are high-frequency and low-frequency channels; Band channels and band termination channels usually require RLC channels, but unrefined channels can be created with RC channels.
Objectives:
The experiment focused on the RC circuit and measure the time constant for the main RC circuit.
Background Theory:
When showing the possible electrical contrast V between the two terminals of a capacitor of capacitance C, the two terminals accumulate charges of opposite sign but equal magnitude, q = V/C. In an idealistic situation for a fully isolated capacitor, this changes q as soon as V changes. One can charge or discharge the capacitor immediately! Practically speaking, you can never test on a single capacitor. Also, isolated capacitors are not very useful.
Now consider a large RC circuit (Figure 1) consisting of a capacitor with capacitance C and a resistor with resistance R. Due to resistance, the current (I) in the circuit cannot be infinitely large. Thus, the capacitor discharge/charge is not instantaneous (Wilson & Hernández-Hall, 2014). At such a voltage, a larger R results in a simpler I and a longer discharge/charge time in that direction. To change the voltage across the capacitor by the same degree, a larger C causes a larger difference in q and therefore a longer discharge/charge time. Therefore, a larger R or C requires more series time for the RC chain. Such a connetion makes stable weather a controlled and useful frontier.
Some of the useful equation for RC time constants are:
𝑉𝑐 =𝑄/C
𝐼(𝑡)𝑅 = 𝑉𝑐(𝑡)
𝑄(𝑡)= 𝑄0𝑒^−𝑡/RC
𝐼(𝑡)= 𝐼0𝑒^−t/ RC
(𝑑𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔): 𝑉𝑐(𝑡)= 𝑉o𝑒^−𝑡/RC
(𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔): 𝑉𝑐(𝑡)= 𝑉𝑆(1−𝑒^−𝑡/𝑅𝐶)
(𝑐ℎ𝑎𝑟𝑔𝑖𝑛𝑔): 𝐼(𝑡)= 𝑉𝑆/R e^-t/RC
Experimental Procedure:
The first step that I took was set up the RC circuit with R=100 Ω (Figure 2(a)) then I connected the shift lead S1 (charge) S1 to the positive battery lead (approximately 3.0V) charging as DC power supply, and connect the switching lead S2 (discharge) to the battery ground wire. The warning considered for this step was that volts above 5.00 V would make the capacitor to dissolves. Secondly, the center wire SO of the double throw change was connected to the positive pole of the ammeter before connecting the unfavorable pole of the ammeter to the positive pole of the 1.0 F capacitor and the negative pole of the capacitor to the open wire of one of the two 100ω resistors (Wilson & Hernández-Hall, 2014).
Another resistor wire was then connected to S2 and through this wire goes to battery ground.
Finally, I connected the voltmeter and capacitor according to the correct polarity. The specialist was then asked to thoroughly check the circuit. While undertaking this process, the charge capacitor was connected to the 100Ω resistor
I then set correct ammeter and voltmeter awareness while one support checks the clock and the other at the ammeter and voltmeter and records the readings in Table below. When finished, the clock was started at t=0 and the double change was reversed from S0 to S1. This starts the loading system.
TABLE 1: Charging capacitor connected to R = 100ω
|
t (s ) |
I (A ) |
V |
t (s ) |
I (A ) |
V |
|
|
|
(V ) |
|
|
(V ) |
|
5 |
25.2 |
0.29 |
210 |
3.0 |
2.70 |
|
30 |
19.6 |
0.98 |
250 |
2.3 |
2.78 |
|
60 |
14 |
1.55 |
300 |
1.4 |
2.87 |
|
90 |
10 |
1.96 |
350 |
0.9 |
2.92 |
|
120 |
7.2 |
2.25 |
400 |
0.6 |
2.95 |
|
150 |
5.3 |
2.46 |
500 |
0.3 |
2.98 |
|
180 |
4.0 |
2.59 |
600 |
.2 |
3 |
For the third step, the capacitor was disconnected to the 100Ω resistor while holding for another 2 minutes. Again, one support would check the clock and the other reviews the voltmeter and record the readings in Table 2. When we were ready, the clock was started at t=0 and the doubled change was simultaneously reversed in S2. This step aided restarting of the release system.
TABLE 2 Discharge of the capacitor connected to R = 100ω
|
t (s ) |
V |
t (s ) |
V |
|
|
(V ) |
|
(V ) |
|
5 |
2.7 |
210 |
0.29 |
|
30 |
2.06 |
250 |
0.19 |
|
60 |
1.48 |
300 |
0.12 |
|
90 |
1.03 |
350 |
0.08 |
|
120 |
0.74 |
400 |
0.05 |
|
150 |
0.54 |
500 |
0.02 |
|
180 |
0.39 |
600 |
0.01 |
The fourth step involved setting the RC circuit with R=50 (Figure 2(b)), changing step 1 unless R=100Ω was replaced with R=50Ω (by connecting two 100Ω resistors evenly) and removing the ammeter from the circuit. Ask your vet to take a close look at the circuit. Once this step was complete, the capacitor connected to the 50Ω resistor was charged. Like in the previous steps, one support experimenter would check the clock and the other the voltmeter while recording the readings in Table 3. The clock was then started at t=0 and while the change in double step S1 was reversed all the time. This starts the loading system.
TABLE 3 Charging the capacitor connected to R = 50
|
t (s ) |
V |
t (s ) |
V |
|
|
(V ) |
|
(V ) |
|
5 |
0.42 |
105 |
2.75 |
|
15 |
0.98 |
120 |
2.82 |
|
30 |
1.6 |
135 |
2.87 |
|
45 |
2.02 |
150 |
2.91 |
|
60 |
2.33 |
180 |
2.95 |
|
75 |
2.52 |
210 |
2.98 |
|
90 |
2.64 |
250 |
3.0 |
Data and Graphs
1. Charging the RC circuit to R = 100
Using Table 1, draw VC-versus-t and install the bend according to equation (5) VC(t) A (1 e Bt) with assembly limits A V0 and B 1 / RC.
Figure 1: The graph of VC-against t
Using Table 1, plot I-versus-t and consider bending according to Equation (3′) I(t)
Ae with adjacent boundaries A V0/R and B 1/RC.
Notice assembled V0/R = 26.6/100 ohms = 0.266 01 = RC = 94.46
2. Discharging the RC element with R = 100
Using Table 2, draw a graph of VC - versus t and adjust the deflection according to Equation; VC(t) Ae Bt with installation limitations A V0 and B 1 / RC.
Note assembly 01 = RC = 90.3
Figure 2: The graph of VC against t
3. Loading RC circuit for R = 50
Using Table 3, draw VC-versus-t and assemble the bend according to Equation (5).
VC(t) A(1 e Bt) with adjacent boundaries A V0 and B 1/RC.
Note assembly 02 = RC = 39.2
Results
The information obtained is very broad because it is still within normal limits. When the capacitor is charged, the voltage increases dramatically in 600 seconds and rises to the ends. On release the opposite occurs, there is a dramatic reduction from the start and smoothing towards the end. This level indicates that the battery is fully charged or empty. At the point where the resistance is lower, the battery can be charged faster as shown in Table 3. This shows that if we assume that there is a higher R or C, the steady time of the RC circuit will also be greater. Most likely the error in this lab may be due to human error.
Conclusion
This experiment indicates that RC circuits can be used to transmit signals by ramming at certain frequencies and across other frequencies. The two most normal RC channels based on this experiment are high-frequency and low-frequency channels. Also, the band channels and band termination channels require RLC channels, but unrefined channels can be created with RC channels. The findings from this experiment indicates that the capacitor discharge/charge is not instantaneous. Another conclusion from this experiment is that at such a voltage, a larger R results in a simpler current and a longer charge time in that direction.
Reference
Wilson, J. D., & Hernández-Hall, C. A. (2014). Physics laboratory experiments. Cengage Learning.
Appendix 1: Data for Charging Time Constant
Appendix 2: Data for Discharging Time Constant
Charging the RC Circuit to R=100
Computed Vc(V) 10 20 30 40 50 60 12.64 17.29 19 19.63 19.86 19.850000000000001
Discharging the RC element with R=100
Computed V 10 20 30 40 50 60 7.36 2.71 0.99 0.37 0.13 4.9000000000000002E-2
