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Name________________________________ Date_________________ Partner(s)______________________
______________________
Physics Laboratory
The RC Series Circuit
The figure below shows an RC series circuit with a battery of voltage Vo and a SPDT switch. A voltage
detecting device is connected across the capacitor.
up
SPDT
R
down
Red
voltage
C
to:
Vo
detecting
Black
device
At time t = 0, the switch is moved to the “up” position. In this case, the charges will be delivered to the
capacitor and we say that the capacitor “is charging.” Without looking at your notes or the text, deduce
and write the equation for the voltage across the capacitor as a function of time.
actual equation for the voltage across the
capacitor
deduced voltage across the capacitor
Now suppose we move the switch to the “down” position. In this case, the charges leave the capacitor
and we say that the capacitor is “discharging.” If we reset the time to t = 0 when the switch is moved
down, then deduce and write the equation for the voltage across the capacitor as a function of time.
actual equation for the voltage across the
capacitor
deduced voltage across the capacitor
For the capacitor charging and discharging, write the value of the voltage across the capacitor in terms of
Vo. Do this at times t = 0, and after a time equal to one time constant, two time constants, three time
constants, four time constants, and five time constants. Generally, we say that the voltage has reached its
final value after a time equal to five time constants.
t=0
charging
discharging
1
2
3
4
5
In this experiment, we will graph the voltage across a 1.00 F capacitor while it is charging and
discharging when connected to a resistor. The experimental time constant, found from the graph and by
curve-fitting, will be compared with the theoretical time constant.
Equipment and Supplies needed




voltage probe
Universal Laboratory Interface (ULI)
Logger Pro 2.2.1
2 D cells with battery holder




SPDT switch
1 Farad capacitor
1-ohm and 2 -ohm resistors
connecting wires
The Experiment
1.
Connect the circuit as shown in the figure above with the 1.00-F capacitor and the 1.00- resistor.
Record the values of your resistor and capacitor in your data table, as well as any tolerance values
marked on them.
2.
Connect the Voltage Probe to the ULI and across the capacitor, with the red (positive lead) to the
side of the capacitor connected to the resistor. Connect the black lead to the other side of the
capacitor.
3.
Prepare the computer for data collection by opening “Exp 27” from the Physics with Computers
experiment files of Logger Pro 2.2.1. A graph will be displayed. The vertical axis of the graph has
voltage scaled from 0 to 4 V. The horizontal axis has time scaled from 0 to 10 s.
4.
Click
to begin data collection. As soon as graphing starts, throw the switch to its “up”
position to charge the capacitor. Your data should show a constant zero value initially, and then an
increasing function. Allow the data collection to run to completion.
5.
To compare your data to the model, select only the data after the potential has started to increase by
dragging across the graph; that is, omit the constant portion. This time you will compare your data
to the mathematical model for a capacitor charging,
t
V (t )  Vo 1  e RC  .


Click the curve fit tool, , and from the function selection box, choose the Inverse Exponential
function, A*(1 – exp(–C*x)) + B. Click
and inspect the fit. Click
to return to the main
graph window.
How is fit constant C related to the time constant of the circuit?
6.
Record the value of the fit parameters in your data table. Notice that the C used in the curve fit is
not the same as the C used to represent capacitance. Compare the fit equation to the mathematical
model for a charging capacitor.
7.
Print the graph of potential vs. time.
8.
Now you will examine the discharging capacitor. Since the capacitor is already charged, click
to begin data collection. As soon as graphing starts, throw the switch to the other position
(“down”) to discharge the capacitor. Your data should show a constant value initially, then a
decreasing function.
9.
To compare your data to the model, select only the data after the potential has started to decrease by
dragging across the graph; that is, omit the constant portion. Click the curve fit tool , and from the
function selection box, choose the Natural Exponential function, A*exp(–C*x ) + B. Click
, and
inspect the fit. Click
to return to the main graph window.
10. Record the value of the fit parameters in your data table. Notice again that the C used in the curve fit
is not the same as the C used for capacitance. Compare the fit equation to the mathematical model
for a capacitor discharge proposed in the introduction,
V(t )  Vo e
 t RC
.
11. Print the graph of potential vs. time.
12. Now repeat the experiment with a different resistor. How do you think this change will affect the
way the capacitor discharges? Rebuild your circuit using the new resistor and repeat Steps 4 – 11.
Data Table
Curve Fit Values
Trial
A
B
C
Resistor
Capacitor
R ()
C (F)
Charging 1
Discharging 1
Charging 2
Discharging 2
Analysis
1.
Calculate and enter into the results table the theoretical time constant of the circuit using your
resistor and capacitor values.
2.
Calculate the inverse of the fit constant C (1/C) for each trial and enter them as curve-fitting
determined time constants in the results table.
3.
On each of your four graphs, choose an arbitrary starting point for the charging and discharging
curves and treat that point as time t = 0. From this point, find the 63% voltage position for the
charging situation and the 37% position for the discharging situation, and find the time it takes to
reach those voltages. Enter these time values as the graphically-determined time constants, and
place them in your results table.
4.
Now compare each of the graphically-determined values to the time constant with the theoretical
time constant by calculating a percentage error. of your circuit by calculating a percentage error.
Trial
Theoretical
Time Constant
(s)
Curve Fit
Time Constant
(s)
Percentage
Error
Graphical
Time Constant
(s)
Percentage
Error
Charging 1
Discharging 1
Charging 2
Discharging 2
5.
Note that the resistors and capacitors are not marked with their exact values, but only approximate
values with a tolerance. If the tolerance is taken into account, does the amount of error between the
theoretical and experimental values of the time constant decrease.? If so, show an example;.