Physics 196 Laboratory 7: R-C Time Constant and Oscilloscope
Materials (12 teams, 2 students/team): Each team needs a RIGOL DS1102E 100 MHz Digital
Oscilloscope (with power cord), a PASCO Function Generator (with voltage converter and power cord),
an Oscilloscope probe, a pair of banana to alligator leads, a small breadboard, 2 short wires, 3 capacitors
(0.1 μF, 1μF and 1μF) and 3 resistors (1,000Ω, 3,300Ω and 10,000Ω).
Lab Description: As usual, please include in your laboratory notebook a complete description of what
you are doing, what equipment you are using, how it is configured, what you are trying to achieve, what
your results are, and how they compare to what you were expecting. Make sure to include your raw data
both in tabular form and graphical form (where indicated).
You will work in teams of two, using a function generator to apply a square voltage wave form across a
resistor and capacitor in series, and an oscilloscope to measure the resulting voltage vs. time across the
capacitor. You will observe that the capacitor charges (increasing the voltage across it) or discharges
(decreasing the voltage across it) with a characteristic exponential curve, and you will measure the time
constant of this curve and compare it to theory for different sets of resistors and capacitors.
Figure 1: Equipment for Lab 7, R-C Time Constant and Oscilloscope.
If the voltage across a capacitor and resistor in series is suddenly switched from V0 volts to 0 volts, it will
take time for the capacitor to discharge and lose the voltage across it. (As a circuit element, a capacitor
resists a change in voltage). As a function of time, the voltage across the capacitor will be V(t) = V0e-t/RC
where R is the value of the resistance (in ohms) and C is the value of the capacitance (in Farads). 1ΩF =
1 second. Similarly, if the voltage across the resistor and capacitor in series is suddenly changed from 0
volts to V0, the voltage across the capacitor will be V(t) = V0(1-e-t/RC). The value RC is the time constant
for charging or discharging the capacitor.
Prelab: Calculate the RC time constants for all combinations of 1 resistor and 1 capacitor from the
values given in the materials list, and list them in a table. (There are nine possible combinations of R and
C, but some of the time constants will be the same). Pick one of these R-C pairs, and assuming an initial
voltage of 4V across the pair in series, carefully plot the expected voltage as a function of time across the
capacitor if at t=0 the voltage across the resistor and capacitor in series is suddenly switched to 0V. Your
horizontal scale (time) should extend for 4 time constants, and use most of the width of the lab notebook.
Your vertical scale (voltage) should extend from 0 to 4V, and use about ½ of the height of the lab
notebook page. Plot at least 15 points extending evenly across the range of time values. Calculate and
mark carefully on the graph the values for the voltage when t/RC =1 and when t/RC =2. (You will need
these values for the lab). If your plot is not similar in shape to what is shown on the oscilloscope trace in
figure 1 there is something wrong.
Lab: Carefully lay out the equipment on the lab bench. Plug in the Oscilloscope using the grey power
cord, and plug in the function generator using a power cord and the black power converter. Connect the
voltage output of the function generator to the breadboard using red and black banana-to-alligator leads,
with short wires running from the red alligator clip to the (+) strip running down one length of the
breadboard, and from the black alligator clip to the (-) strip running down the length on the other side.
All the holes down the length of the breadboard on the two sides (marked + and -) are connected together
in a line. On the interior part of the breadboard, for each row number, (f,g,h,i,j) are connected together,
and (a,b,c,d,e) are connected together (but not connected to f,g,h,i,j). Thus, it is easy to connect circuit
elements together as desired by sticking their leads into the appropriate holes in the breadboard.
Start with the 1000Ω resistor and the 0.1μF capacitor which should give the shortest time constant
(100μs). Hook the resistor from a hole on the (+) voltage column to an interior position in one of the
rows. Hook the capacitor from the same row (such that it is electrically connected to the resistor) to the
(–) voltage column. (Note, the 0.1 μF can be attached in either direction, but the 1μF and 10μF capacitors
are designed to prefer one side at the lower voltage as marked on the capacitor with a – sign). Set the
oscilloscope probe on the 1x setting (yellow switch towards the tip of the probe). Connect the probe tip
to the resistor wire entering the (+) voltage column, and the black alligator lead to the capacitor wire
entering the (-) voltage column. Attach the BNC connector end of the oscilloscope probe to CH1 (X) on
the oscilloscope. Turn on the Function Generator and the Oscilloscope. The Function Generator should
turn on in its default mode showing a 1000 Hz sine wave with 0V. The oscilloscope remembers its
previous settings. Let’s hope it does not take too long to get to the settings we want.
Turn the voltage knob on the function generator two clicks to the right so the dsiplay reads 2.00 V peak.
This should give an output sine wave of 4 V peak to peak at 1000 Hz. (1 Hz = 1 cycle per second, so the
sine wave should make a complete cycle 1000 times per second, giving it a period of 1 ms). We want to
display this sine wave on the oscilloscope. (At this time we should be measuring the output of the
function generator which is applying a voltage across the R-C combination in series. We will measure the
voltage just across the capacitor later).
If the oscilloscope is set up properly, it should be automatically triggering on the voltage signal coming
into channel 1. (This means it should always start the trace at the same voltage, and then a repetitive
signal should appear fixed on the screen). Adjust the left scale knob until the CH1 setting is 1.00V per
division, and adjust the left position knob to center the trace on the screen. Adjust the right scale knob to
200 μs per division. You should see two periods of a sine wave on the screen. If you are not seeing that,
or if there seems to be too much other information on the screen, call for help!
Once you have a signal, you should observe the effect of adjusting a limited number of parameters. The
oscilloscope is a device which displays the input voltage as a function of time. If the input voltage
changes, so should the display. Similarly, if the frequency of a repetivite input signal changes, so should
the display. The function generator frequency is changed by using the two buttons below the frequency
knob to adjust the underlined digit in the frequency display, and then turning the frequency knob. The
voltage is changed in a similar way with the voltage knob. The oscilloscope voltage scale and time scale
are changed with the left and right scale knobs on the oscilloscope. Change the input frequency and the
oscilloscope time scale over the range which you think you will need to observe the different time
constants you calculated in the prelab. Write a paragraph in your notebook discussing the different
adjustments you are making (staying on the sine wave).
Now go back to 1000 Hz (or 1 kHz) on the function generator and press the waveform button. Adjust the
voltage knob so the arrow points to “Square” and press the voltage knob to select. Now you should be
outputting a square wave. Set the voltage to 2.00V peak. Now press the menu button, and the arrow
should point to V Offset. Select this and turn the knob for a 2.00 V offset and push to select. Press menu
again to get back to the output display, which should be for a 2.00 V Peak, 2.00 V offset, 1000 kHz
square wave. This should go from 0 to 4 V and back. Verify with the oscilloscope that this is the output
of the function generator. For the rest of the lab you will only change the frequency, leaving the square
wave function and voltage constant.
With the oscilloscope time scale on 200 μs per division and the voltage scale on 1.00 V per division,
sketch the pattern you see on the oscilloscope (a square wave). Now move the oscilloscope probe so it is
attached to the resistor or capacitor wire in the middle of the RC series circuit. The pattern on the
oscilloscope should look different, with the capacitor alternately charging and discharging with the
characteristic exponential decay shape. Sketch what you see in your lab notebook. Have the instructor
verify that everything is set up and working properly before going to the next step.
To accurately measure the RC time constant, change the oscilloscope voltage scale to 0.5V/division (so 4
V takes up the whole vertical scale) and change the time scale to 50μs per division. Adjust the horizontal
position so the voltage starts its fall from 4 V at the first division mark (50 μs in). Adjust the vertical
position so the 4V level is at the top line on the oscilloscope, and the 0V level is on the bottom line. (See
figure 1). Now use the cursors to make time constant measurements. When you hit the cursor button, a
menu should come up on the screen saying “Cursors”. Use the blue button to select X Type, and then
alternately CurA and CurB. Set the time position of Cursor A using the knob (above the CH1 button) so
that it is just at the time when the voltage starts to drop. Ajudst the time position of Cursor B so that it
intersects the voltage deacay curve at the 4V/e (as calculated in the prelab). Record the time
measurement (ΔX) between the cursors displayed on the screen. This should be 1 RC time constant.
Make a second measurement at 2 RC time constants (where the voltage has dropped to 4V/e2). Have the
instructor check your measurements. They should agree fairly well with your calculations.
Now make a table with 6 columns. They should be R, C, calculated RC time constant, measured time to
1/e (1 time constant), measured time to 1/e2 (2 time constants), and percent error between measured and
calculated time constant. Make measurements for the 9 R-C combinations by substituting different
resistors and capacitors in the circuit breadboard, and fill in the table. (You will have to vary the input
waveform frequency and oscilloscope time scale over a fairly wide range to make the measurements.
Make sure the input frequency is low enough so that the capacitor is fully charged before the discharge
cycle.)
Have fun, and try to get a good understanding of the exponential R-C decay curve and how to use the
oscilloscope. Be sure to write a complete description of the experiment in your lab notebook, including
materials used, labelled experimental diagram including electrical connections, procedures, results and
conclusions.