Lab Physics Lab 8 Capacitance and the Oscilloscope
Aleksey Zelenberg
Introduction
This experiment was aimed at measuring the RC constant (also called the time constant) of various circuit setups (Figs 1 & 2 below). The experiment consisted of two parts. In the first part, we measured the current on five-second time intervals while charging and discharging the capacitor. In the second part, we utilized the Tektronix TDS-210 Digital Oscilloscope to measure a much smaller time constant. Our results in the first part indicate a similarity between the time constants obtained from charging and discharging. Our measured results () from the second part statistically agree with the calculated results (RC).
Procedure Fig 1i
Fig 2
The experiment consisted of two parts. In the first part, we used a combination of resistance and capacitance chosen specifically so that the time constant is long enough to allow for current observation with an ammeter. Using this setup (Fig 1), we were able to measure the time required for the current to reach 20 A, 15 A, 10 A, 5 A. We then plotted log I vs. t (since it is an exponential function and a linear fit is required) to obtain the slope and y intercept. We then used the equation to obtain I0 and the time constant (RC).
In the second part, we utilized a digital oscilloscope to directly measure the time constant. After varying the frequency of the function generator to obtain multiple results (to obtain a statistical accuracy), we measured how much time was required for the voltage to drop to 37% of its initial value (this is ). Finally, we computed the time constant directly by multiplying C (8.2*10 -8 F) and R (10 k + 50 ii) and compared it to the value of we had previously attained.
Results Part 1 Large RC Charging 10 F: I0 = 24.1476 0.3008 A; RC = 5.5629 0.0742 s 20 F: I0 = 24.8846 0.2303 A; RC = 11.1139 0.1082 s 30 F: I0 = 24.2113 0.6244 A; RC = 17.5815 0.484 s Large RC Discharging 10 F: I0 = 24.4660 0.1780 A; RC = 5.7115 0.0458 s 20 F: I0 = 24.8780 0.1830 A; RC = 11.0270 0.0840 s 30 F: I0 = 24.4385 0.3606 A; RC = 17.3027 0.2691 s Part 2 Observation of Short RC Time RC = 824.1 s avg, w = 7.5 831.43 s Discussion Part 1 Although the time constants do not agree within errors, they are very similar. For the 10 MFd capacitor the time constants differed by approximately 3%; for the 20 MFd capacitor the time constants differed by approximately 1%; for the 30 MFd capacitor, the time constants differed by approximately 2%iii. Although the relatively small errors on the time constants do not
allow the results from the RC charging and RC discharging to agree within error, the percent differences shown above demonstrate the precision of the experiment. Since our circuit was not connected to any timer mechanism and all time measurements were made with a stopwatch, the statistical discrepancies between the results for charging and discharging are most likely due to random human errors associated with operating the stopwatch. However, the values for initial current (I 0) agreed within error for charging and discharging the capacitor. Part 2 As demonstrated in the Error Range on graph, the calculated value of RC statistically agrees with the value obtained from the oscilloscope. Interestingly enough, although the impedance of the oscilloscope was merely 0.5% of the 10 K resistor used, adding it to the total resistance allowed for our calculated RC value to fall within the error range of the time constant . Without this small addition, RC would be 820 s, a value that is outside the error range of 831.43 7.5 s for . Conclusion The two parts of this experiment were extremely informative and insightful on how electric circuits and specifically capacitors operate. Our results in the first part, while statistically inconsistent (do not agree within error), are relatively close (see discussion Part 1). The second part produced extremely accurate results. This is most likely due to the high degree of accuracy obtained by using a sophisticated digital apparatus. Overall, the experiment was a huge success.
i
Images obtained from course website The added 50 comes from the impedance of the oscilloscope iii These calculations were made by choosing one time constant as the "accepted value" and computing the percent difference of the two.
ii