the rc circuit

#$&*

Phy 232

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 V, 140 ohms

24.25781, 4

54.32813, 3.5

94.82813, 3

143.5156, 2.5

202.7969, 2

282.7734, 1.5

391.6641, 1

476.4531, .75

587.5938, .5

702.75, .25

The data above shows the decrease in the voltage across a capacitor when it is connected in series to a resistor. The data also shows that the voltage decreases at a decreasing rate.

** #$&* 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. **

172.8 seconds

173.3 seconds

Using excel, a scatter plot of the data was made and then fit with a trendline of an exponential function. Then, using this equation for the line of best fit, the voltage values were filled in and the equation was solved for time.

** #$&* Table of current vs. clock time using same resistor as before, again starting with 4 volts +- .02 volts. **

14.07031 seconds, 15 mA

48.71094, 12

123.4844, 9

215.8438, 6

340.7188, 3

** #$&* Times to fall from initial current to half; 75% to half this; 50% to half this; 25% to half this, based on graph. **

138.6 seconds

As described previously, these values were found using the equation of the line of best fit from the excel graph of the data.

** #$&* 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? **

All of the values are the same; however, the values for the current measurements are slightly lower than the values for the voltage measurements.

** #$&* Table of voltage, current and resistance vs. clock time: **

56.5 s, 3.53 V, 12 mA, 294 ohms

114 s, 2.80 V, 9 mA, 311 ohms

195 s, 2.03 V, 6 mA, 338 ohms

334 s, 1.16 V, 3 mA, 387 ohms

472 s, .669 V, 1.5 mA, 446 ohms

** #$&* Slope and vertical intercept of R vs. I graph; units of your slope and vertical intercept; equation of your straight line. **

-13.602, 440.89

ohms/mA, ohms

R=-13.602I+440.89

The equation of this line was found by creating a graph with the data above on excel. The negative slope of the graph indicates that as current increases, resistance decreases.

Your data would indicate that. Resistance should increase with temperature, and temperature increases with current. However there might be other factors associated with the capacitor and/or the generator.

** #$&* Report for the 'other' resistor:; Resistance; half-life; explanation of half-life; equation of R vs. I; complete report. **

** #$&* Number of times you had to reverse the cranking before you first saw a negative voltage, with 6.3 V .15 A bulb; descriptions. **

The cranking had to be reversed only three times before a negative voltage was registered. As soon as the direction was reversed, the bulb dimmed because the voltage across the capacitor was moving toward zero.

** #$&* When the voltage was changing most quickly, was the bulb at it brightest, at its dimmest, or somewhere in between? **

It appeared that the bulb was in between when the voltage was changing most quickly. This occurs because a large portion of the voltage is still going through the capacitor because a large charge has not yet been built up across the plates of the capacitor.

** #$&* Number of times you had to reverse the cranking before you first saw a negative voltage, with 33 ohm resistor; descriptions. **

The direction of the cranking only had to be reversed one time before a negative voltage was observed.

** #$&* 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. **

7 beeps, 4.2 seconds

** #$&* Voltage at 1.5 cranks per second. **

4 V

** #$&* Values of t / (RC), e^(-; t / (RC) ), 1 - e^(- t / (RC)) and V_source * (1 - e^(- t / (RC) ). **

1.2, .301, .699, 2.796

** #$&* 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): **

2.796, 4

** #$&* According to the function V(t) = V_source * (1 - e^(- t / (RC) ), what should be the voltages after 25, 50 and 75 'beeps'? **

1.04, 1.80, 4

** #$&* Values of reversed voltage, V_previous and V1_0, t; value of V1(t). **

** #$&* How many Coulombs does the capacitor store at 4 volts? **

** #$&* 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?; **

** #$&* 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? **

** #$&* 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? **

** #$&* How long did it take you to complete the experiment? **

2 hours