Ph 213 General Physics III Lab PCC Cascade page 1 of 5 Experiment Capacitance OBJECTIVES Compare the relationship between charge flow and time varying electric potential for a capacitor Explore the relationship between charge accumulation and electric potential for a capacitor Calculate compare calculated capacitance values with direct measurement MATERIALS Logger Pro software 10 F non polarized capacitor LabPro Interface connecting wires Vernier Current Probe Pasco Electric Circuit Board Analog Out Connector Vernier Voltage Probe INTRODUCTION For a charging capacitor the accumulation of electric charge is related to the increase in electric potential across the plates dq C dV Dq CDV Note when Vo 0V V V and therefore q CV Dividing this equation by dt leads to dq dV i t C dt dt where C is a proportionality constant called the capacitance measured in the unit of the farad F 1 F 1 C V that describes the physical properties of the system to accumulate electric charge Thus the rate of charge movement is proportional to the rate of change of the potential difference across the capacitor i t C V t Figure 1 The electric potential energy stored in the capacitor at any time t can be described in terms of the capacitance and the potential difference across the capacitor U t 1 2 CV 2 Ph 213 General Physics III Lab PCC Cascade page 2 of 5 PRELIMINARY QUESTIONS 1 The potential difference across the plates of a 10 F capacitor varies sinusoidally between 10V and 10V at a cycle frequency of 50 Hz a Express the equation for potential difference in the form V t Vmax sin t b Determine the equation for the capacitive current i t What is the maximum rate of charge flow imax c What is the maximum rate of charge flow i max for this varying potential difference d Sketch a plot of V t and i t vs time e Determine the maximum amount of charge accumulation q max and maximum stored energy U t on the capacitor at Vmax 2 The potential difference across the plates of a 100 F capacitor increases linearly with time from 0V to 10V over an interval of 5x10 3s then decreases linearly with time from 10V to 0V in the same amount of time a Write out the equation for potential difference V t b Determine the equation for the capacitive current i t c Sketch a plot of V t and i t vs time d How much charge is stored in the capacitor at the end of 5x10 3s Ph 213 General Physics III Lab PCC Cascade page 3 of 5 PROCEDURE 1 Obtain an Analog Out connector and plug it into the LabPro interface in Ch 4 2 Connect the Current Probe into Ch 1 and the Differential Voltage Probe into Ch 2 3 Start up the LoggerPro software then open the capacitance experiment file located on the network drive 4 The Ch 4 connector will allow the LabPro interface to operate as a time varying voltage source Open the Set Up Sensor window and select Ch 4 Analog Out 5 In the Analog Out window select Triangle waveform and select Create User Parameters then close the window 6 In the main screen verify that the Analog Out frequency is set to 150 Hz set the amplitude 1 with step size should be set to 0 5 7 Click on the Data Collection button and verify that the data sampling rate is set to maximum 5000 points second Close the Data Collection window 8 With the current probe open and the voltage probe terminals connected to each other Zero the probes 9 Construct a circuit as shown in Figure 2 using a 5 to 10 F capacitor Locate several connecting wires with alligator clips Liberal use of these connecting wires will make connecting the circuit more tenable Be sure to attach a wire with alligator clip to each of the voltage probe terminals This will make connecting the voltage probe easier Current Probe Analog Out C Voltage Probe Figure 2 The Circuit Note the Current Probe must be connected in series with the voltage source analog out wires and the capacitor 10 Attach the Voltage Probe across the terminals of the capacitor 11 Click to begin data collection Verify that the potential difference is a triangular function and that the current is roughly a square wave If the voltage and current graphs look screwy no would be the time to attempt to fix it Question Why the current be expected to look like a square wave Ph 213 General Physics III Lab PCC Cascade 12 page 4 of 5 Now that things are working properly set the Amplitude to 0 5 and collect a data trial for voltage and current If the data looks appropriate choose Store Latest Run 13 Repeat step 6 for amplitude values of 1 2 3 and 4 14 Cut and paste the graph of V vs time and I vs time for Amplitude 1 only into Microsoft Word 15 Using a digital multimeter directly measure capacitance of the capacitor Record the value in Table 1 ANALYSIS 1 Comparison of I vs dV dt 1 Measurement of dV dt For Run 1 Amplitude 0 5 use the Linear Fit function to measure the slope of the voltage vs time graph Repeat for a downslope region of the graph Record the dV dt values and uncertainty in Table 1 2 Measurement of iavg For Run 1 Amplitude 0 5 use the Statistics function to measure the average current value corresponding to each dV dt value in 1 Record the iavg values and uncertainty in Table 1 3 Repeat steps 1 and 2 for each of your stored data runs DATA TABLE 1 Amplitud e Measured Capacitance C dV dt dV dt iavg iavg dV dt dV dt iavg iavg 4 Using Graphical Analysis create a graph of i avg vs dV dt including error bars Plot both the positive and negative values To plot error bars add 2 new manual data columns for dV dt and i avg and enter the corresponding uncertainty values In the column options window you can set the Error Bar Calculations to use the corresponding data column 5 Fit the graph to an appropriate function probably a linear fit Record the slope and y intercept values for the graph Then calculate the Error between the measured capacitance and the slope of the graph Slope Y Int Error Ph 213 General Physics III Lab PCC Cascade page 5 of 5 ANALYSIS 2 Comparison of q vs V use same data as above 1 Measurement of V For Run 1 Amplitude 0 5 use the Statistics function to measure the minimum and maximum voltage for a region where the voltage increases from minimum to maximum Repeat for a downslope region of the graph Record the V values and uncertainty in Table 2 2 Measurement of q For Run 1 Amplitude 0 5 use the Integral function to measure the area under the current vs time graph i e the total charge for each current step corresponding to the V values in 1 Record …