Lab Report 4
RC Time Constant
Physics 262-003
Author: A. Coughran
Lab Partners: E. Ortiz, H. Barham
Date: 4/5/17
Lab Report 4 A. Coughran 4/5/17
Objective:
The objective in Lab 4 is to measure the RC time constant for a capacitor in a series RC circuit with a resistor. This will be accomplished by the analysis of voltage curves across the resistor.
Theory:
Kirchoff’s Voltage Law states that the voltage sum across a series circuit containing one resistor and a capacitor must be zero. The formula for voltage on a capacitor is defined below in Equation 1, and the formula for voltage on a resistor is defined below in Equation 2. A combination of these equations yields a formula that correctly expresses Kirchoff’s
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In Logger Pro, the data collection time was set to 3-4 seconds and the sample rate was set to 1000 samples/second. The voltage on the capacitor was tested and then zeroed before beginning data collection.
Next, the power supply was unplugged and the supply voltage (V_0) was set to 5V. Data collection was started and graphs of voltage vs. time were collected. The power supply was re-connected to the circuit after about one second after starting the data collection. This small time delay allowed for the charging curve in the graph to be seen visually with more ease and represent accurate data.
This same process was repeated 5 total times for several voltage vs. time curves, and the data was saved in Logger Pro for inclusion in the data section after taking curve fits of the data.
Data:
A graph visually depicting each of the 5 runs of voltage vs. time. A table representing the numerical data of voltage vs. time for each of the 5 runs above. Procedure A represents the theoretical value for the time constant through the use of the formulas in the theory section, while Procedure B represent the experimental value for the time constant by taking the curve fit of the collected data.
Analysis:
Procedure A
The time the voltage was applied, the time at which the switch was closed, and the time at which the voltage reached one-half of its maximum value after switch closure were calculated for each of the 5 runs above. Using this experimental data, the time
Factory calibration was used for the thermistor. Time was placed on the horizontal axis of the graph, and temperature on the vertical axis. The digital precision was set at two digits past the decimal point.
Only three peaks were identified from the data and four were supposed to appear; 1,4-dichlorobutane was missing on the data. Reading from the handout that was posted online with an example GC run, the fourth peak is not on the graph because the GC was cut off too soon. In the example, the last peak came up around retention time 8.5. According to this data, GC was cut off around retention time 8.0. Another issue is that the second peak, 1,2-dichlorobutane to be precise, is very little. That is it is not even registered in the data. Due to not having the full data, the example GC run is used for this lab report.
\emph{Testing Strategy:} The graph between applied load in the range 0.5 grams to 575.5 grams and change in voltage is plotted. The graph obtained (see Figure~\ref{f:olggraph}) shows the inconsistent readings at many points for different combination of force applied. Also, the best curve equation is close to cubic, which is indication of bad design.\\*
Table 1: This table shows the position that the solution was at inside the graduated tube it was held in at each time interval it was measured.
For the first part of the lab, our goal was to calculate the time constant, , of an RC circuit. We made an RC series circuit and connected it to the Rigol wave generator to produce a square waveform for current. Then, we collected data of the voltage across the capacitor at different points in time using a myDAQ and the 4BL application. In order to find the time constant, we linearized the voltage we measured across the capacitor and then performed a linear regression on the data. The equation for the voltage across the capacitor as a function of time is:
A differential equation for the equivalent circuit can be derived by using Kirchoff's voltage law around the electrical loop. Kirchoff's voltage law states that the sum of all voltages around a loop must equal zero, or
Introduction: Voltage can be thought of as the pressure pushing charges along a conductor, while the electrical resistance of a conductor is a measure of how difficult it is to push the charges along. Using the flow analogy, electrical resistance is similar to friction. For water flowing through a pipe, a long narrow pipe provides more resistance to the flow than does a short fat pipe. The same applies for flowing currents: long thin wires provide more resistance than do short thick wires. The resistance (R) of a material depends on its length, cross-sectional area, and the resistivity (the Greek letter rho), a number that depends on the material. The resistivity
2. Try increasing the resistivity of the resistor, ρ. How does this change the “look” of the resistor? Describe how that relates to the formula you just wrote (direct, indirect relationships, etc.). What happens to the value of “R” (Resistance)? Is this something that can be changed in a resistor that you would buy in a store to use in a circuit?
Theoretical analysis is one of the most significant phases of the project. The high resistance measurement system developed during this project is primarily based
Boylestad, Robert L. Introductory Circuit Analysis, VitalSource for DeVry University, 12th Edition. Pearson Learning Solutions, 11/2012. VitalBook file.
Figure.10 (a) Hardware test bench set up (b) Gating pulses for 70 KHz from DSP processor (c) Input voltage and input current waveforms for 230Vrms (d) Input voltage and input current waveforms for 110 Vrms
The mean voltage of the battery terminals while connected to the identification resistors is presented in Figure 4 12. These samples have been pulled out from the voltage sensor of the PEB panel. The voltage decreased as expected from 12.53 to 12.5 during first 20 seconds of connection to the
The table below represents the average samples processed per hour and per step, based off the minimum, average, and maximum samples processed on exhibit 4. Separation numbers are half of the other process’s sample numbers because only 50% of samples go to separation.
Use a stopwatch to time 5 cycles and record the time in the data table.
Empty and clean the test tubes and repeat steps 2-10 again for a second dataset.