Lab 5: EC-3, Capacitors and RC-Decay Lab Worksheet

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1 , Capacitors and RC-Decay Lab Worksheet Name 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. The procedure for this lab is changed slightly from the lab manual. We use a circuit board in which you can easily build a circuit by plugging in elements to a board, rather than connecting them with wires. The board is shown below: Resistor or capacitor block goes here These 5 points connected together Holes connected by black lines are electrically connected by wires, so all points connected by black lines are at the same electric potential. You build a circuit by plugging in resistors or capacitors across the gap between crosses. The resistors and capacitors are built into plastic blocks with banana-plug connectors that exactly bridge the gap. The hole spacing on the circuit board is such that the resistors and capacitors will fit only between holes that bridge a gap. After you plug in a resistor or capacitor to bridge the gap between crosses, there will still be unused holes in each cross. You will connect the variable supply and various meters to these remaining holes as needed to supply to your circuit, and to measure potential differences and currents at various points in the circuit. There are four parts to the lab: PART A: build two resistor circuits, investigating current flow and s. PART B: build two capacitor circuits, investigating how charge distributes. PART C: build a resistor-capacitor circuit, investigating how a capacitor charges up. PART D: Build cell membrane electrical model, investigate propagation of an action potential.

2 A. Resistor circuits i) Measuring current and. Build the circuit below. Here the wire block is a plug-in block that is a metal conductor. Keithley DMM The digital mulitimeter (DMM) can be configured to measure current,, and resistance. Here you want to measure current. Press the A button for amps, then 2m for a 2 ma scale. The DMM now acts as an ammeter, and it displays how much current flows through it. In this mode it is very low resistance. So it acts like a connecting wire while measuring current, and doesn t alter the properties of the circuit. Current flowing into the red terminal of the DMM and out of the black terminal gives a positive reading on the display. Set the supply to 20V and measure the current through the circuit. Explain your result. 2

3 ii) Now you will add a 100KΩ resistor in parallel to this one and measure the current. Before you do this, predict your measured current in the space below. Now build the circuit as shown: Wire Wire Keithley DMM What is your measured current? Explain whether this agrees or disagrees with your prediction. 3

4 iii) Voltage drops around the circuit, and measuring current with drops. In part ii) you saw that the DMM can measure current directly, but it must be inserted in the path of the current so that current can flow through it. This makes it difficult to quickly probe current in different parts of the circuit. If you press the V button, the DMM will display the electric potential difference between its red and black terminals. In this mode, almost no current at all flows through the DMM it acts like an extremely large resistor while measuring. Explain how you use the DMM to measure the current through a resistor by measuring electric potential difference ( drop) between the two ends of the resistor. Now make the circuit below R1 R2 Use the voltmeter to determine the current through each of the resistors. Write the current below. Current through R1: Current through R2: 4

5 In the next step you will put a 100KΩ resistor (call it R3) in parallel with R2. But before making the circuit, predict whether the currents through R1 and R2 will increase or decrease. Current through R1: Current through R2: Explain: Now build the circuit as below, and determine the currents with the voltmeter. R1 Wire R2 Wire R3 Voltage across R1: Current through R1: Voltage across R2: Current through R2: Voltage across R3: Current through R3: Explain how this agrees or disagrees with your prediction. Now draw a path through the circuit starting at the red terminal of the power supply and ending at the black terminal. Measure the drops across each of your plastic blocks along this path and add them up. What do they add up to? Explain. 5

6 B. Capacitor circuits. These are the same experiments as in the lab manual, but with instructions for the new circuit board. You use the electrometer to measure s, not the Keithley DMM. You will need to connect the red and black needle probes to the electrometer with coaxial (BNC) cables. i) Series capacitors: you will build the circuit below and measure it, but first predict how the 20V provided by the supply will split among the two series capacitors. V across C1: V across C2 Explain: Build the circuit below (note that the power supply is not connected) µf C1 1.0 µf C2 Measure the drops across the capacitors. a) First, use a bananna plug cable to temporarily short out each capacitor to make sure there is no charge separation between the plates. Make sure the cable is removed before proceeding. b) Set the supply to 20V, and briefly touch the black and red leads across the series circuit, then remove the connection. c) Use the electrometer (not the Keithley DMM) to measure the drops across each capacitor individually. Compare these to your prediction. 6

7 ii) Parallel capacitors. Here you connect capacitors in parallel to see how they share charge. You first charge up C1 (the 0.5µF capacitor) to 20V, then disconnect the supply. You then connect the 1 µf capacitor in parallel (after making sure the 1 µf capacitor is discharged). Do a calculation here to predict the final across the capacitors. Now do the experiment: 0.47 µf Wire C1 Wire 1.0 µf C2 Plug 1 µf capacitor in after making sure it is discharged, and after disconnecting the power supply. Measure the drop across the parallel combination with the electrometer (not the DMM). Remember that the power supply is disconnected here. How does this compare with your predicted value? 7

8 C. Resistor-capacitor circuits. Now you will connect a resistor and capacitor to investigate how a capacitor charges and discharges. Turn the on and set it for zero volts output. Connect the and electrometer to the 10 MΩ resistor and 1 µf capacitor as shown below. For the electrometer, use a BNC to banana plug adapter connected to the input : - + Electro meter 10 MΩ 1 µf Put the electrometer on the scale, and make sure the is still at zero V. Quickly increase the on the supply to 20 V and watch the electrometer. After the electrometer needle stops moving (you ll probably need to wait at least a minute), quickly turn the supply to zero volts, and watch the electrometer again. Note that the electrometer measures the sign as well as the magnitude of the across the resistor. Remember that the supply keeps a constant between its two output terminals. Zero volts means that there is no potential difference between the red and black terminals: it is as if they are connected by a wire. Describe the current in the circuit after your sudden increase / decrease. Where is this current going? The current varies in time. If you had to describe the time dependence to someone with a single time, what would that time be (i.e. how many seconds?). How did you decide this? 8

9 Now use the computer to measure the time-dependent current through the resistor. Use the same capacitor, but a 100 kω resistor instead of the 10 MΩ resistor. Explain how this change will affect the time-dependence of the current. Pasco interface A - + Differential amplifier Switch 100 kω 1.0 µf The Pasco interface will measure the drop across the resistor, but it needs to be isolated with the differential amplifier to get quantitative results here. Set the amplifier to a gain of 1 (1X setting). The amplifier needs to be plugged in and turned on. Set the supply to 10V, and set the switch to its open position. The switch is on a small board with banana-plug connectors in the parts tray. Start DataStudio by clicking on the Lab5Settings1 file on the Laboratory page of the course web site. Use DataStudio to measure the time-dependence of the current through the circuit when you close the switch and then open it again. Describe the results here. 9

10 You have measured vs time, but want current vs time. The conversion factor is the resistance. You can directly scale the plot, or just account for this factor in your area calculation. Use the mouse to select the decay from maximum negative 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 In the space below, calculate the expected value of this area from basic principles of the capacitor (you don t have to do any integration). How does your value compare to the measured one? 10

11 D. Electrical model of a cell membrane You don t need to use the differential amplifiers here, just plug right into the Pasco interface. Exterior of cell A 1 A 2 A 3 A 4 A 5 A 6 Pulse generator 1 µf 1 µf 1 µf 1 µf 1 µf Lipid Bilayer WIRE WIRE WIRE WIRE WIRE B 1 B 2 B 3 Cell membrane equivalent circuit Interior of cell As discussed in class, a cell membrane has a potential difference between the interior and exterior of the cell. The low-resistance cell interior is modeled by a low-resistance wire through which charges move. The medium resistance cell exterior is modeled by resistors. The capacitors model the capacitor formed by the interior and exterior conducting fluids that sandwich the insulating lipid bilayer. The potential difference arises from charges in the conducting fluids that form the electrodes of the cell-membrane capacitor. These charges can move around in the fluids in response to electric fields, with the resistance to their motion given by the resistors/wires above. The result is that an action potential (generated at the left end here) can propagate down the cell membrane. The switch models an ion channel that is triggered by some external stimulus, mechanical, chemical, or electrical. It could be a channel opening in response to a pinprick in your finger. This causes a change in potential difference at that location. No other ion channels are modeled here. In a real cell membrane, there are -triggered ion channels distributed throughout. They open and close in response to varying potential differences across the membrane. That is, their resistance to charge motion varies with they don t obey Ohm s law. We don t model them here because we don t have suitable nonlinear resistors. One of their effects is to bring the potential difference across the cell membrane back to its resting state after reaching a threshold value. This contributes to making the action potential a short pulse. Here we use a pulse generator to artificially introduce the pulse. The sensitive ion channels also serve to propagate the pulse down the cell membrane, keeping a sharp shape via their non-ohmic behavior, and contributing to determining the propagation speed. Here only the contribution from the RC network is modeled, so the pulse broadens and decays. Hodgkin and Huxley shared the 1963 Nobel prize in physiology and medicine partly in recognition of their quantitative analysis of the full nonlinear electrical circuit model. B 4 B 5 B 6 11

12 Making the measurement to determine signal propagation To start the action potential, you want to introduce a pulse at A 1,B 1, and watch it propagate down the cell membrane, similar to an action potential. This pulse then propagates down the cell membrane. If you could measure the potential differences A i,b i at a particular instant in time, you might see something like the following. POTENTIAL DIFF. ( V ) Time t 1 Time t POSITION You can only measure potential differences across the capacitors the squares and triangles represent potential differences measured at these locations. The dashed line is what the pulse might look like in a continuous version of the model. The triangles correspond to the differences at slightly later time ( t 2 ) than the squares ( t 1 ). Data such as this would indicate that the pulse is traveling to the right at some speed. In DataStudio we don t measure all the s at a particular instant in time, but measure each as a function of time. For instance, at position 2, the is large at time t 1 and then smaller at time t 2. The at position 3 is small at time t 1, and has gotten larger at time t 2. Your job here is to reconstruct a graph like the figure above from the vs time data acquired with DataStudio. 12

13 Directions for taking data. You investigate the propagation by measuring the potential differences between the pairs A i,b i with DataStudio. Start DataStudio by clicking on the Lab5Settings3 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 (A 1,B 1 ) 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. First, connect (A 2,B 2 ) and (A 3,B 3 ) to the B and C inputs. You don t need to use the differential amplifier here, because we don t need a quantitative answer like we did in the previous section. You produce the pulse with a timing circuit that produces a single 22 milli-second pulse whenever you push the button. We only have one of these right now, so ask your TA after you have built the circuit, connected the probes, and have DataStudio started with the Lab5Settings3 file from the course web site. Take a measurement by clicking Start on DataStudio, then push the button on the pulsegenerator board. DataStudio stops acquiring data automatically after 2 seconds you don t have to click stop. (A 1,B 1 ) will show you the input pulse, (A 2,B 2 ) is the first capacitor charging/discharging, and (A 3,B 3 ) is the second capacitor charging/discharging. Now connect the B and C inputs to (A 4,B 4 ), (A 5,B 5 ) and repeat the measurement. Finally, connect B and C to (A 5,B 5 ) and (A 6,B 6 ) and take the last measurement. You will now have in DataStudio vs time for all of these positions, 1-6. Now you should pick particular times (use the cross-hair tool), and plot vs position for these times on the plot below. You can do this in Excel if you like. How fast does the pulse propagate? POTENTIAL DIFFERENCE POSITION 13

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