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: **

4.02 volts, 147.7 ohms

3.5 volts, 15.2 seconds

3.0, 17.5+previous time

2.5, 22.6+previous time

2.0, 27.8+previous time

1.5, 35.8+previous time

1.0, 51.7+previous time

.75, 36.9+previous time

.5, 53.6+previous time

.25, 96.5+previous time

** #$&* 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. **

83 seconds

104 seconds

115 seconds

51.7 seconds

The graph looks like an exponential graph with a negative exponent V0*(exp(1/(RC)))

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

s, mA

0, 26

10, 24

20, 22

30, 20.2

40, 18.7

50, 17.2

60, 16

70, 14.7

90, 12.6

120, 10

The capacitor was charged to 4 volts, then stabilized. Then the meter was set to measure mA and the clock was started. The measurement of current was taken at each of the above values.

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

80 seconds

30 seconds

300 seconds

long time

** #$&* 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? **

Both measurements required ~80 seconds to arrive at the value 1/2 of the original.

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

A different technique was used: a line of best fit using excel gave k*exp(-.0077t). This was used to calculate the current for each voltage point measured down to 1v. The following voltage, current, and resistance measurements are the result.

volts, mA, ohms, seconds

3.48, 23.8, 146.2, 12

3.03, 20.4, 148.5, 30

2.5, 16.9, 147.9, 54

2.0, 13.6, 147, 80

1.5, 10.1, 148.5, 160

** #$&* 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 flat line at r~150 ohms for each current.

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

99.81

7 seconds +-.3 seconds

Average, plus or minus variation

R=100

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

4 or 5

It seems to be accurate

The bulb lights up. When reversing, the bulb dims and then lights up again.

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

Brightest

I=C*'dV*'dt, so when 'dV is at a max, current is at a max. Therefor most current flow through the fimliment.

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

** #$&* 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. **

The delay in the clock time will be related to the 1/(RC) time constant.

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

3.5 volts

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

0, 0, 1, 3.5.

I am not sure I did this correctly; I assume that t=0 and that the capacitor was charged fully. Maybe I am missing something?

** #$&* 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): **

3.5, 3.5.

100%

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

.368, .679, 1.3

** #$&* 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? **