Virtual Lab: Capacitors and RC circuits 12.2.1 Goto: httgs:ghet.colurado.edulenlsimulationegacy/circuit-construction-kit-ac-virtual-lab Introduction The objectives of this virtual lab are: 0 to build an RC circuit with switches and DC power supply. 0 to learn the properties a capacitor when it is charging and discharging in RC circuit. 0 to better understand the capacitive time constant by experimentally analyzing the voltage vs time data. To this end, open the link by CLICKING HERE and you see what you see in Fig. 12.9.Download and open the le and it leads you to the simulation window shown in Fig. 12.10. 12.2.2 Part I: Constructing an RC circuit with switches 1. Construct the circuit shown in Fig. 12.11. This diagram shows 3 resisters and one capacitor connected in series, two switches and a battery. Set the battery voltage to V5 = 5V , the capacitance to the maximum value Figure 12.9: Circuit Construction Kit (AC+DC), Virtual Lab 9; Figure 12.10: Opened Circuit Construction Kit. C = 0.2F and the resistance of each resistor to the maximum value R1 = R2 = R3 = 10051 Keep both switches open. Figure 12.11: A direct current RC circuit. For this kit unlike the kit we used in the previous labs, to change the source voltage, the resistance, or the capacitance you right click on the battery, the resistor, the capacitor and small window will be opened where you can select the changes you want to make. Click on the box for a Voltmeter and connect it across the capacitor to get ready for measuring the voltage across the capacitor. You will measure the voltage across the capacitor when it is charging and discharging. (Remember for the voltmeter, the red lead must be connected to the positive side and the black lead to the negative sides of the capacitor). Click on the box for the Stopwatch and reset it to zero to get ready for reading time and the voltage from the voltmeter. You will read every 15 seconds for 8 minutes. The rst 4 minutes is when the capacitor is being charged and the next 4 minutes is when the capacitor is being discharged. Charging: When the rst switch is closed and the second switch is open as shown in Fig. 12. 12, the capacitor is charging. Figure 12.12: The position of the switch when the capacitor is charging. Discharging: When the rst switch is open and the second switch is closed as shown in Fig.12. 13, the capacitor is discharging. Click on the hand of the switch and drag it along the appropriate direction to open or close the switch. Figure 12.13: The position of the switches when the capacitor is discharging. 3. Now you are about to get started recording the voltage reading on the multimeter. For the rst four minutes keep the rst switch closed and the second open. At t = 4 minutes= 2403 open the rst and clothe the second. During the entire 8 minutes you read the voltage every 15 seconds and record the values in the table provided below. It is recommended to pause the simulation at the end of the period for charging (t=240s). You can even pause at every reading and resume when you are ready. 4. In Table 1. Record both stopwatch and the voltmeter readings at every 15 seconds when the capacitor is charging and discharging. Time, t, (in Voltage across the capacitor, V0; (in seconds) volts) 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360 375 390 405 420 435 450 465 480 Estimate the uncertainties for your measurements: Calculated the fractional uncertainties: Turn the power o and show your results to your instructor before you proceed to the next part. 12.3.5 Part III: Analyzing the results . Using XL make a graph for the voltage across the capacitor (AI/C) vs time (t). (All; on the y axis and t on the xaxis). You must get a non-linear graph. The graph displays two parts: an increasing part of the voltage approaching a maximum voltage followed by a decreasing voltage approaching 9\"?" to the zero voltage. The increasing part is when the capacitor is charging and the decreasing part is when it is discharging. We recall that when the capacitor is charging the voltage is given by AV; = VMAX(1 _ 8HT) and when it is discharging it is given by All/"C(t') = AV'Oe'WT' where AV'O is the voltage across the capacitor just before the switch is thrown to E (i.e. at t=4 minutes). Next we will determine the capacitive time constant using the half-life time (t1 [2) for the charging period and the discharging period. You were introduced to half-life time (t1 [2) in radioactive decay activity (Chapter 10). Here the t1=2 is the time it takes for the voltage across the capacitor to reach to half of the measured maximum voltage (when it is charging or discharging). You can determine the value for t1=2 for charging as well as the discharging by following the procedure below similar to what used in Chapter 10: (a) Read the maximum voltage across the capacitor from your graph. (b) Calculate half of the maximum value, Vmax=2. (c) Locate the value for Vmax=2 on your graph. You must be able to locate two points on your graph. The rst is in the charging part and the second is in the discharging part of the graph). Read the time from the time axis for these two points. (d) Find the half-life time for the charging and discharging for charging and discharging. Using the half-life times you determined for charging and discharging, calculate the capacitive time constants along with the uncertainties. Calculate the theoretical value for the capacitive time constant Make a sketch of your graph on the graph paper provided. Optional: By linearizing the discharging voltage vs time data make a linear graph using XL. Find equation for the best-fit line to the linear graph and determine the capacitive time constant along with the uncertainties. Graph title: Y axis title: X axis title: Figure 1223: Graphing page. Result and conclusion 1. Did all the experimentally determined capacitive time constants agrees with theoretical value within the uncertainties? If not explain what you think may be the cause of the disagreement. 2. Write a brief (3-5 sentences) overview of what was accomplished in and concluded in the home virtual as well as classroom activities