You measure the potential difference across a capacitor at different times while

Question

You measure the potential difference across a capacitor at different times while it's charging and record the following results. Voltage (V) Time (s) 1.2790 0.01930 2.6000 0.04506 3.9210 0.08138 5.2210 0.14317 The final voltage the capacitor reaches after you go get some coffee is 6.500 V. (a) Analyze the data. (You will not submit this spreadsheet. However, the results will be needed later in this problem.) (i) Enter the above data into an Excel spreadsheet. (ii) Perform all calculations needed to compute ?ln(Vfinal ? V/Vfinal) for each voltage in this question. (iii) Make a plot ?ln(Vfinal ? V/Vfinal) versus the time. (iv) Use the trendline option in Excel to fit the data of ?ln(Vfinal ? V/Vfinal) versus the time to get the slope. (b) Report this value below. slope = ___ (c) Determine the time constant from the slope. ? = ____ (I keep getting answers that are within 20 percent.)

Explanation / Answer

Voltage Time Ln(Vf - V)/Vf 1.279 0.0193 0.254 2.6 0.04506 0.209 3.921 0.08138 0.146 5.221 0.14317 0.038 6.5 infinity My chart wouldn't copy across but it appears that the slope is about -1.3 so the time constant would be 1.3

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