Charge and discharge of a capacitor lab report

1- the lab manual.

2- Letter on how to write a lab report.

3- Letter on the grading criteria (how the report will be graded).

Capacitance

Capacitors store charge and perform many useful functions in circuits. The charge on a capacitor’s plates is proportional to the potential difference across the capacitor.

(1)

where is a proportionality constant known as the capacitance. Capacitance has units of farads (F) (1 farad = 1 coulomb/volt).

If you imagine a charged up capacitor as being a bunch of electrons on a piece of metal, then you can further imagine that, if a wire is connected to the capacitor, these electrons will want to drain off of the capacitor - and what are moving electrons but current? The capacitor only has a finite capacity for charge, so the current will decrease with time. This process causes the potential across the capacitor to decrease exponentially with time as

(2)

where is the initial potential across the capacitor, is time, is the resistance in the circuit and is the capacitance. The rate of the decrease is determined by the product, known as the time constant of the circuit. When the capacitor is charged, the potential across it approaches the final value following the relation

(3)

As you can see, the same time constant describes the rate of charging as well as the rate of discharging.

For an analogy to this type of exponential decay, imagine a candy jar that is initially filled with 1000 candies and once an hour you eat 10 % of the candies in the jar. Clearly, the 10 % comprises a smaller and smaller number of candies each time. For an exercise, sketch a rough graph of the number of candies vs. time; how would the graph change if instead of 10 %, you removed 20 % at a time?

Learning Goals for This Laboratory:

· Become familiar with the breadboard and connecting simple circuits on it.

· Become familiar with exponential decay including the time constant and the effect of R and C values.

Apparatus
computer with iOLab interface, iOLab remote and dongle, breadboard, wires, 10k Ohm Resistor, 100µF Capacitors

Part I. Setting up and Exploring the Breadboard
Figure 1. A breadboard.

First, we’ll become familiar with the breadboard and measuring voltage using the iOlab remote. Let’s call the iOlab remote “iOlab” for short.

a) If you have not already done so, pull the tab on the back of the iOlab to allow the battery to connect. Turn on the iOlab using the power button on the front.

b) If you have not already done so, download and install the appropriate version of the iOLab app for your computer (http://www.iolab.science/running-application.html).

c) Start the iOlab app. Plug the USB dongle into your computer. If the app does not run because it requires a manual driver installation, the driver can be found here: http://www.iolab.science/driver-installation-windows.html.

d) Now we’ll use the A7 input to measure voltage. In the iOlab app, click on the box labeled Analog 7 to bring up a display of the data measured at input A7, see below.

Figure 2. The iOlab app data display. Analog 7 is selected.

e) If the Record button is grayed-out, the iOlab likely went to sleep, so power it on again. Click Record and you should see the default voltage at A7 is about 1.6 V.

f) Now take a jumper wire from the set you received with your electronics supplies (the jumper wires can be peeled apart). Plug one end of the wire into the 3.3 V output of the iOlab and the other end into the A7 input. With the data recording, watch the A7 reading on your computer as you plug and unplug the wire into the A7 input. Is the 3.3 V measured at A7?

g) Watch the short video here briefly describing the iOlab and how to use it to explore the breadboard.

https://www.youtube.com/watch?v=ERCLlfAnSZ4

h) We will now explore the breadboard as in the video; the steps are as follows. The goal is to make a sketch of which pinholes on the breadboard are electrically connected to each other behind the scenes. For example, are pinholes a1 and a2 connected? Are all the pinholes on column a connected? What do the positive and negative signs indicate on the breadboard?

Figure 3. Setup for probing the breadboard.

To do this plug one the wire from the 3.3 V output on the iOlab into one of the points in the left-most column of the breadboard (the one labeled with the + sign). This provides 3.3 V to the board. Now plug a second wire into the A7 input of the iOlab, and your setup should look like that in the figure at right.

i) Use the second wire as a probe to check if the 3.3 V appears at other pinholes on the board. For example, check other pinholes on the positive column, the negative column and other places on the breadboard. Then move the 3.3 V wire from the + column to a different place on the breadboard, say a1, and again probe the voltage around the breadboard to see which points are connected to a1 electirically. Continue to use trial and error and your deductive skills to map out the internal connections of the breadboard.

j) In the data section of your report, include a rough schematic showing all the connections between the pinholes on the breadboard. You can sketch it by hand or find an image of a breadboard and use word, powerpoint, photoshop, etc to indicate the connections.

Part II. Charging and Discharging a Capacitor
a) Build the circuit as shown in Figure 4 with the C = 100 µF capacitor and R = 10 k resistor. Instead of the the 3.3 V, the power source will be pin D6 on the iOLab, the wire attached to the A7 sensor should connect between the resistor and the capacitor, and the circuit must be grounded back into the iOLab. This video will help guide you through the construction of this circuit

https://www.youtube.com/watch?v=vGCx1KnlR4I&feature=youtu.be

Make sure when building your circuit that you note the polarized nature of the capacitors, denoted by the long and short ends. The long end is the positive end, which should be connected to the resistor, whereas the short end should connect to the ground.

b) In order to control the output voltage of pin D6, you also need to click the settings button dropdown, go to the Expert Mode sidebar, and click Output Config. This will bring up a set of buttons below the graph options that have “On/Off” and “0/3.3V” toggles.

Figure 4. Circuit with resistor and capacitor in series. Image source: Hayden-McNeill

Data Collection
a) Set the Output Configuration to 3.3V and On. Click Record and watch as the capacitor charges for 30 seconds or so. You should see the voltage reading increase over time, if not, toggle the output on again.

b) Now turn the Output voltage to 0 and observe the curve of the voltage graph as the capacitor discharges. Note that when the data reaches the right-most edge of the graph, it will start again at the left end. Although your data seems to disappear, you will see it again once you stop recording.

c) Fully charge and discharge the capacitor a few times so that you have at least one set of clean data, i.e. no kinks or discontinuities. Once you have sufficient data, hit Stop.

Question 1. How do the shapes of the charging and discharging compare? Use the concept of “like charges repel” to explain why it gets harder and harder to increase the voltage on the capacitor as more charge is placed on it.

d) If you get your resistors mixed up and do not know how to tell them apart, check out this guide to reading the color bands http://www.resistorguide.com/resistor-color-code/

Data Analysis
Now we’ll fit the discharging data to an exponential function and compare the result to Equation 2 above.

a) Export the data to a .csv file by clicking on this button at the bottom of the A7 graph:

Click “Export to CSV” and note the save location indicated by the popup box (it should save in your documents folder to a subfolder called “IOLab-WorkFiles”)

b) Open Pasco Capstone and select File Import Data. Change the filetype to .csv and navigate to the IOLab-WorkFiles folder. You should find your .csv file in the export folder. Select it and confirm to import the data.

c) In Capstone, create a graph of the voltage vs. time by creating a new graph, and the clicking Select Measurement, then under user-entered data select “cal[0]” which is the voltage data. For the time axis, be sure to graph the user-entered time, not the generic time. You should see a reproduction of the charging and discharging graph you saw in the iOlab app.

d) Drag the axes of the graph or scroll to zoom in on the section of the data where the capacitor was charged and discharged. Use the highlighter tool to highlight the data in the graph for the discharging process. Adjust the size of the highlighter box to only include the smooth middle section of the discharging, avoiding the discontinuity when the voltage was switched off.

Coordinate Tool

Fitting Tool

Highlighter

e) Use the fitting tool to fit the data to a natural exponential function of the form .

Question 2. Compare the fit function parameter in the equation above to the time constant in Equation 2. What is the equation for in terms of and ?

f) Given the resistor and capacitor values we used, calculate the expected time constant of the circuit; make sure to use SI units. Compare this to the actual time constant you measured by calculating percent difference.

Question 3. About what percentage of the initial voltage remains after one time constant has passed? After two time constants?

g) Calculate the energy in Joules stored in the capacitor when it is fully charged. Refer to your textbook if you need the formula for the energy in a capacitor.

h) Calculate the charge in Coulombs on the capacitor when it is fully charged.

Question 4. Look closely at the capacitor. Even though it’s cylindrical in shape, it’s a parallel plate capacitor made of two sheets of foil rolled up into a tube. See the diagram below. Estimate the length of one sheet of the foil inside the capacitor by using the parallel plate capacitance equation and assuming the dielectric (the oxide layer) has a dielectric constant of 8 and the gap between the foil plates is 50 micrometers.

Electrolytic Capacitor » Capacitor Guide