Your 'the rc circuit' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Your comment or question: **
** Initial voltage and resistance, table of voltage vs. clock time: **
4.00
0,4.0
10.45,3.5
24.25,3.0
41.55,2.5
62.53,2.0
90.75,1.5
131.8,1.0
160.4,0.75
201.6,0.50
** Times to fall from 4 v to 2 v; 3 v to 1.5 v; 2 v to 1 v; 1 v to .5 v, based on graph. **
62
66
69
69
The graph is decreasing at a decreasing rate. It is a curve because a line did not seem to fit the data well. I picked the two points on the graph and found the difference in time between the points.
** Table of current vs. clock time using same resistor as before, again starting with 4 volts +- .02 volts. **
0,38
8.797,35
20.75,30
36.17,25
54.84,20
81.45,15
119.3,10
187.9,5
260.3,2.5
339.7,1.25
The above current vs clock time data was obtained by placing a ammeter in series with a capacitor and resistor. The current was measured in mA.
** Times to fall from initial current to half; 75% to half this; 50% to half this; 25% to half this, based on graph. **
60
57
70
70
The graph of current vs time is again decreasing at a decreasing rate. I picked the two points on the graph and found the difference in time between the points.
** Within experimental uncertainty, are the times you reported above the same?; Are they the same as the times you reports for voltages to drop from 4 v to 2 v, 3 v to 1.5 v, etc?; Is there any pattern here? **
The times appear to be very similar with the exception of the second time.
** Table of voltage, current and resistance vs. clock time: **
20,3.2,0.03,106.7
48,2.4,.0228,105.3
79,1.6,.0152,105.3
150,0.8,.0076,105.3
208,0.4,.0038,105.3
The resistance was obtained by dividing the voltage observed at the given time by the current observed at the given time. The values for voltage and current were taken from graphs that try to model the data points.
** Slope and vertical intercept of R vs. I graph; units of your slope and vertical intercept; equation of your straight line. **
The graph is a line with a slope of 1 that passes through 105.3. I thought that the data point at 106.7 was an error considering the other data points were the same. This means that the resistance is constant.
** Report for the 'other' resistor:; Resistance; half-life; explanation of half-life; equation of R vs. I; complete report. **
22
15 +- 4.243
I took the times to drop to half the voltage and half the current and found the mean and std. deviation. `dt is the std. deviation.
I think the equation for this line is between x=19.73 +- 2.637. This value is the mean of the values of the resistance.
** Number of times you had to reverse the cranking before you first saw a negative voltage, with 6.3 V .15 A bulb; descriptions. **
10
I think I was within a couple of iterations.
When reversing the crank, the work was being done with an opposing charge and reduced amount of energy in the capacitor.
The bulb started out at about medium brightness and faded out. When the cranking reversed, the bulb went to maximum brightness. When it reversed back to the way I originally cranked, it dimmed.
** When the voltage was changing most quickly, was the bulb at it brightest, at its dimmest, or somewhere in between? **
The bulb was at its brightest when the voltage was changing most quickly. Work was being done at a greater rate which would lead to greater voltage per unit charge.
** Number of times you had to reverse the cranking before you first saw a negative voltage, with 33 ohm resistor; descriptions. **
8
I think the estimate was accurate.
The voltage in the capacitor decreased with time.
** How many 'beeps', and how many seconds, were required to return to 0 voltage after reversal;; was voltage changing more quickly as you approached the 'peak' voltage or as you approached 0 voltage; 'peak' voltage. **
25,14.7
It changed more rapidly as approaching 0.
3.5
** Voltage at 1.5 cranks per second. **
3.5
** Values of t / (RC), e^(-; t / (RC) ), 1 - e^(- t / (RC)) and V_source * (1 - e^(- t / (RC) ). **
2.67,0.0690,.931,3.26
** Your reported value of V(t) = V_source * (1 - e^(- t / (RC) ) and of the voltage observed after 100 'cranks'; difference between your observations and the value of V(t) as a percent of the value of V(t): **
3.26,3.5
7.4
** According to the function V(t) = V_source * (1 - e^(- t / (RC) ), what should be the voltages after 25, 50 and 75 'beeps'? **
1.71,2.58,3.03
** Values of reversed voltage, V_previous and V1_0, t; value of V1(t). **
-3.5,3.5,-6.5,14.7
.235
I plugged the values into the reversed equation. This is the value of the function at the time that I saw a negative on the voltmeter. If my observations matched with the calculations, the value should have been negative. It is fairly close.
** How many Coulombs does the capacitor store at 4 volts? **
4
1F * 4V = 1C/V * 4V = 4C.
** How many Coulombs does the capacitor contain at 3.5 volts?; How many Coulombs does it therefore lose between 4 volts and 3.5 volts?; **
3.5,0.5
There are (1C/v * 4.0V) - (1C/V * 3.5V) = 4.0C - 3.5C = 0.5C
** According to your data, how long did it take for this to occur when the flow was through a 33-ohm resistor?; On the average how many Coulombs therefore flowed per second as the capacitor discharged from 4 V to 3.5 V? **
2.45,.204
The first is the time, according to my measurements to drop from 4.0V to 3.5V through a 22 ohm resistor (there was no 33 ohm resistor). The second value is the result of dividing 0.5C/2.45s = .204 Amps. This seems rather high as to what I observed.
** According to your data, what was the average current as the voltage dropped from 4 V to 3.5 V?; How does this compare with the preceding result, how should it compare and why? **
.153
This seems much lower than what was calculated. They should be very close, but are not. I had problems getting a reliable measurement in resistance vs current, but the calculation at the top of the curve was very close to what the resistor is rated.
** How long did it take you to complete the experiment? **
About 10 hours
** **
I had a hard time getting reliable results with the 22 ohm resistor especially in the resistor vs. current. I conducted that portion of the experiment a couple of times and couldn't get it to work out any better.
Very good. I don't see any obvious error in your analysis of the data related to the 22 ohm resistor; it appears you did everything right.