Resistor Capacitor and Circuits - Lab 6 | PHYSICS 208, Lab Reports of Physics

Download Resistor Capacitor and Circuits - Lab 6 | PHYSICS 208 and more Lab Reports Physics in PDF only on Docsity! Name _______________________________ Section ___________ Physics 208 Fall 2008 Lab 6: Resistor-Capacitor (RC) Circuits Your TA will use this sheet to score your lab. It is to be turned in at the end of lab. You must use complete sentences and clearly explain your reasoning to receive full credit. What are we doing this time? You will complete two related investigations. PART A: Build resistor-capacitor circuits, and measure time-dependent phenomena. PART B: Use these ideas to measure and investigate a cell membrane electrical model, investigating propagation of an action potential down the cell membrane. Why are we doing this? Capacitors are almost as ubiquitous as dipoles, showing up almost everywhere there is an insulator. Actually, capacitors have some similarities to dipoles, with equal and opposite charges on the electrodes. And they almost always show up in combination with some non-insulator — a resistor-capacitor circuit! What should I be thinking about before I start this lab? You should be thinking about the ideas of circuits you developed when looking at resistors and capacitors last week. In particular, how the voltage across the capacitor is related to the charge on it, and how the current in a circuit delivers charge to a capacitor. Lab 6 2 For the first part of the lab, you use the same circuit board as you did last week. The board is shown below: Holes connected by black lines are electrically connected by conducting wires, so all points connected by black lines are at the same electric potential. You build a circuit by plugging in resistors and capacitors across the gap between crosses. The resistors are built into plastic blocks with banana-plug connectors that exactly bridge the gaps. After you plug in a resistor, there will still be unused holes in each cross. You will use the remaining holes to connect the variable voltage source to supply your circuit with charge, and to connect the Keithley DMM or Pasco interface to measure currents and potential differences at various points in the circuit. These 5 points connected together Resistor or capacitor block goes here Lab 6 5 Now you do use the computer to measure the time-dependent current through the resistor. Use the 1 µF capacitor, and the 100 kΩ resistor. To make an accurate measurement, the voltage needs to be switched very quickly from 0V to 10V (the Pasco can measure only up to 10V), more quickly than you can do it by turning the knob. Set up the circuit below in order to quickly switch the voltage, with the power supply at 10V. The switch is in the parts tray. 1) What will be the potential difference between points A and B when the switch is … a) all the way to the right? b) all the way to the left? The Pasco interface measures the voltage drop across the resistor, and hence can tell you the current through the circuit. Start DataStudio by clicking on the Lab6Settings1 file on the Laboratory page of the course web site. Use DataStudio to measure the time-dependence of the current through the resistor when you flip the switch all the way to the left, then all the way to the right, repeating several times. Your switch may have a center position — we don’t use this position. 2) Describe the data on the computer you have obtained. Explain Switch A B 100KΩ 1. 0 µF Wire Pasco interface A 30V DC voltage source 1000V Lab 6 6 3) What is your maximum measured current, and when does it occur? 4) Directly from the data on the computer, determine the time constant τ of the circuit. 5) Calculate the time constant from the resistor and capacitor values and compare to your measurement in 4). In this part you determine how much total charge has flowed through the resistor. You have measured voltage vs time, but in order to measure the total charge you will need current vs time. The conversion factor is the resistance. You can directly scale the plot in DataStudio, or just account for this factor in your area calculation. 6) Use the mouse to select the decay from maximum to zero current on your Current vs Time (sec) graph, and find the area under the curve by selecting ‘area’ from the ‘statistics’ (capital sigma) pull-down menu at the top of the graph. Area under curve Value Units 7) In the space below, calculate the expected value of this area from how the charge on the capacitor is related to its electric potential (you don’t have to do any integration). How does your value compare to the measured one? Lab 6 7 Now think about this circuit, but don’t build it or measure it. Why would you ever care about this circuit? Be patient — in the next section you use this as a basis for a model of a nerve signal (action potential) propagating down a cell membrane. 1) Suppose the capacitors start out discharged, and you apply 10V across the circuit. At the instant you apply the voltage, what are the currents through R1 and R2? 2) Where does the charge flowing at this instant end up? 3) Think about later time intervals. Why does C1 charge up sooner than C2? If the voltage rising above some threshold value across each capacitor triggered something to happen, then that event would occur sooner at C1 and some time later at C2. In this way you can think about this as a signal propagating down the circuit (e.g. an action potential). In the next section you watch a voltage pulse propagate down a similar circuit. R1=100 KΩ C1=1 µF C2=1 µF R2=100 KΩ Lab 6 10 Directions for taking data. You investigate the propagation by measuring the potential differences between the pairs Ai,Bi with DataStudio. Start DataStudio by clicking on the Lab6Settings3 file on the Laboratory page of the course web site (We are not using LabSettings2 right now). DataStudio has three analog inputs A, B, and C. The potential difference at (A1,B1) measures the pulse before it propagates down the cell membrane. This must always be connected to input A because DataStudio watches this input to determine when to start recording data. You measure the other potentials with inputs B and C. To start, connect (A1,B1) to the A input, and (A2,B2) and (A3,B3) to the B and C inputs. You start a pulse moving down the membrane by generating a single short pulse at one end. After you have the circuit, connected the voltage probes, and have DataStudio started with the Lab6Settings3, go get a pulse generator and plug it into your board. Set your voltage supply to 12V, and connect it to the red and black terminals of the pulse generator (if you don’t get the polarity right you’ll burn out the chip. But don’t worry — it’s easy to replace.) If you don’t think you can set it up, ask your TA. This is what you need to do to acquire the voltage across each capacitor: 1. Start by clicking ‘Start’ on DataStudio. 2. The program is now waiting for you to push the pulse-generator button. Push the pulse-generator button just once, and watch the data roll in. DataStudio stops acquiring data automatically after 2 seconds — you don’t have to click stop. 3. This is the data you have so far: Input A [(A1,B1)] shows you the input pulse, Input B [(A2,B2)] is the first capacitor charging/discharging, and Input C [(A3,B3)] is the second capacitor charging/discharging. 4. Now connect the B and C inputs to (A4,B4), (A5,B5) and repeat the measurement (remember to keep (A1,B1) connected to input A so it can trigger the data acquisition). 5. Finally, connect B and C to (A5,B5) and (A6,B6) and take the last data. (remember to keep (A1,B1) connected to input A so it can trigger the data acquisition). 6. When you have finished, put your pulse generator back in the box so someone else can use it. Lab 6 11 You will now have in DataStudio voltage vs time for all of these positions, 0-5. Look at the data, and answer the following questions. 1) What is the duration and amplitude of the original voltage pulse? 2) What is the potential difference between A1 and B1 before, during, and after the pulse? 3) How does this compare to the experiment you were doing on page 5 when you used the switch from the parts box? 4) Why do the potential differences across the capacitors start small, increase, then decrease again? 5) Why do the potential differences across capacitors farther down the cell membrane reach their maximum later than the ones closer to the pulse generator? 6) Suppose a pulse were propagating down the cell membrane. How would the voltage vs time across one of the capacitors look? Lab 6 12 Now you see if there is a pulse that propagates down the cell membrane, and how fast it moves. To do this, pick three different times at which to plot voltage vs position on the plot below (see figure page 9). You can use the cross-hair tool to find values of the voltage across each capacitor at these three times. How fast does the pulse propagate? SPATIAL POSITION 0 Cap. 1 Cap. 2 Cap. 3 Cap. 4 Cap. 5 P O TE N TI A L D IF FE R E N C E