Capacitance resistance τ expected τ measured

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Capacitance Resistance τ (expected) τ (measured) Amplitude (V 0 ) Table 1: The expected value of τ comes from the model described by Eq. 4. The measured τ and amplitude are determined by fitting this model to your data runs. Figure 3: Driven RC Circuit (series) 8.1 Collecting Data For this section you will be using the following components: resistors (100, 560, 1 3 , 1 × 10 4 Ω) and capacitors (100, 330 μ F). Locate these and measure their values. 6
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To keep track of your measurements form a table similar to Table 1. Calculate the values you expect for τ , from theory, for each pair of R and C values and record them in your table. Now assemble a series RC-circuit (Figure 3) using the first resistor/capacitor pair in your data table. Connect the Pasco Voltage Probe in parallel with the capacitor (shown in Figure 3). Set the Signal Generator to output a DC voltage of 3V. De-select the ‘Auto’ option in the Signal Generator window so that you can manually turn on and off the applied voltage. When you’re ready to begin collecting data open a ‘Graph’ window and click start at the top of the main DataStudio window. Shortly after clicking ‘Start’ click ‘On’ on the Signal Generator window to apply the DC voltage. The graph should display a real time plot of the voltage across the capacitor (Figure 4). Figure 4: Plot of capacitor voltage vs. time Once the voltage across the capacitor has stabilized switch off the DC voltage. The capacitor voltage should then decay back to zero. Once it has done so, click ‘Stop’. To make an accurate measurement of τ it would be prudent to fit the model for the capacitor voltage to the data observed (Eq. 4 or 5) and from this extract the fit parameter representing τ . This would be the most accurate way since it utilizes the entire data set. BUT a much quicker method (which you will use here) is to note the following: when t τ = RC in Eq. 5 then V(t) t τ V 0 e - 1 0 . 368V 0 (6) Thus by measuring the time difference between the maximum voltage and the point at which the voltage is 37% of this max one can get an approximate value for τ , as shown 7
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Figure 5: A detailed view of the discharging portion of Figure 4 showing how to make an approximate measurement of τ . in Figure 5 (NOTE: t = 0 is defined as the time at which the voltage is switched ‘On’ or ‘Off’ and not necessarily the zero point on your data graph). Save the data, to be used later in your lab report. Repeat this process for all other combinations of R and C . Compare these values to the theoretically calculated values for τ . Would your measurements of τ have been different had you used a larger DC voltage? 8.2 MATLAB Fitting Now make a plot of τ vs. R for the data corresponding to each capacitor.
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