Name___________________ ID number_________________________
Date____________________ Lab partner_________________________
Lab CRN________________ Lab instructor_______________________
Physics 2306
Experiment 7: Time-dependent Circuits, Part 1
Objectives
•
•
To study the time dependent behavior of the voltage and current in circuits
containing a capacitor, a resistor, and a voltage source (“RC circuits”)
To gain familiarity with the operation of two very useful test instruments – the
digital oscilloscope and the function generator
Required background reading
Young and Freedman, section 26.4
Introduction
In the last two labs, you studied circuits where the current and voltage were constants
(independent of time). In this lab, you will study circuits where the current and
voltage vary with time. For circuits where the voltage varies in a rapid way, there is
an essential piece of electronic instrumentation that is needed. It is called an
oscilloscope. Generally it is used to display voltage (on the vertical axis) versus time
(on the horizontal axis).
The time dependent circuits you will look at in this lab will contain capacitors,
resistors and a voltage source. Capacitors are devices that store electric charge (and
therefore energy).
Consider the series circuit depicted in Figure 1. It contains a resistor and a capacitor.
When the switch is in position 1, current flows from the power supply to the circuit,
thus charging the capacitor. When the switch is in position 2, the power supply is
removed from the circuit, and the capacitor is allowed to discharge through the
resistor.
1
1
2
+
+
DC power
supply
VP
_
Figure 1 A simple RC circuit.
Initially, consider the switch to be in position 2 and the capacitor in Figure 1 to be
uncharged. If the switch is flipped to position 1 to a DC power supply with voltage V0,
the charge will build up according to the charge build-up relationship derived in Section
26.4 of Young and Freedman (equation 26.12). Since the voltage across the capacitor is
proportional to the charge on it (V=Q/C, where C is the capacitance), we have:
t
−
⎛
⎞
V (t ) = V0 ⎜⎜1 − e RC ⎟⎟
⎝
⎠
(build - up)
As discussed in your textbook, there is a characteristic time that it takes to charge (or
discharge) a capacitor. This time depends only on the characteristics of the elements of
the circuit (the resistor and capacitor) and not on the applied voltage. A convenient place
to analyze the time to charge the capacitor is to look at the time when t = RC. When
t = RC the voltage equation above becomes,
RC
−
⎛
⎞
RC ⎟
⎜
V (t ) = V0 ⎜1 − e ⎟ =
⎝
⎠
(
V0 1 − e −1
)
We define this interval of time as the “RC time constant” of the exponential charging
function and give it a special symbol τ, where τ = RC. If R is given in ohms and C is
given in farads then τ will be in seconds. A simple evaluation of the equations above
shows that after one RC time constant has elapsed, the voltage across the capacitor has
built up to 1 − e −1 = 0.63 , or 63% of its final value of V0. As you know from your study
of exponential functions the voltage approaches the final value of V0 asymptotically.
Theoretically, after an infinite time the voltage is equal to V0. From a practical point of
view the voltage reaches V0 after a few time constants have elapsed. This is clear if you
look at Table 1 and Figure 2. These indicate the percent of the maximum voltage, V0 ,
2
that is achieved after a certain number of time constants have elapsed. Note that the
curve shown in Figure 2 is a universal curve. Once you know the RC time constant of a
circuit, this curve gives you everything you need to know about its time behavior during
charge build-up.
Exponential Growth
100%
% of maximum value
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
Time constants
Figure 2: Voltage exponential build-up (growth) curve in an RC circuit.
Table 1: Behavior of growth and decay curves as a function of the number of time constants.
Number
of time
constants
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
% Decay
%
Growth
100.00%
60.65%
36.79%
22.31%
13.53%
8.21%
4.98%
3.02%
1.83%
1.11%
0.67%
0.41%
0.25%
0.15%
0.09%
0.06%
0.03%
0.00%
39.35%
63.21%
77.69%
86.47%
91.79%
95.02%
96.98%
98.17%
98.89%
99.33%
99.59%
99.75%
99.85%
99.91%
99.94%
99.97%
3
After the voltage across the capacitor has settled at its asymptotic value, the switch is
flipped to position 2. This creates a circuit with just a capacitor and resistor, and the
capacitor then discharges through the resistor. The charge on the capacitor will decay
according to the charge decay relation derived in Section 26.4 of Young and Freedman
(equation 26.16). As above, we will monitor the charge on the capacitor, by measuring
the voltage across it. The voltage as a function of time during the decay is given by:
V (t ) = V0 e
−
t
RC
(decay)
As with the voltage build-up, the voltage decays to zero with the same characteristic RC
time constant. After one RC time constant has elapsed, the voltage across the capacitor
has decayed to e −1 = .37 , or 37% of its initial value of V0. Once again, theoretically it
would take an infinite time for the voltage to reach zero, but for practical purposes the
voltage reaches zero after a few RC time constants have elapsed. This is clear if you look
at Figure 3 and Table 1. Once you know the RC time constant of a circuit, this curve
gives you everything you need to know about its time behavior during charge decay.
Exponential Decay
100%
% of maximum value
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Time constants
Figure 3: Voltage exponential decay curve in an RC circuit.
4
8.0
Name___________________ ID number_________________________
Date____________________ Lab partner_________________________
Lab CRN________________ Lab instructor_______________________
Physics 2306
Experiment 7: Time-dependent circuits, Part 1
Ph 2306 Experiment 7: Prelab assignment (complete and turn in at the
beginning of your lab session)
1. Consider the build-up of the charge on a capacitor as described in the introduction to
this lab. Assume that you start with an initially uncharged capacitor, as in Figure 1 and
then you close the switch to a battery of voltage V0. After that time, how many time
constants must elapse before the charge reaches 39%, 63%, and 86% of its final value?
(You do not need to do an exact calculation here; just estimate from the table or curve in
the introduction)
2. For the same case you were considering in problem 1, assume that the capacitor is now
fully charged. Now the switch is flipped (in Figure 1) to position 2, and the charge on the
capacitor begins to decay away. After that time, how many time constants must elapse
before the charge reaches 61%, 37%, and 13% of its initial value (the value right before
you flipped the switch to position 2)? (You do not need to do an exact calculation here;
just estimate from the table or curve in the introduction).
5
3. In lab, you will be building a circuit like that shown in Figure
R
1 in the introduction, but you will want to flip between position
1 and position 2 much faster than you can do by hand. Instead,
V(t)
C
Vout
you will be using a function generator to deliver an input voltage
V0
GND
, which alternately steps
known as a square wave
between zero and some constant value V0. This is equivalent to
regularly switching between a position 1 (V0) and position 2
(zero) of Figure 1 on page 2 of this writeup. Use the formulae on pages 2-4 of this
writeup to predict the time dependent behavior of the voltage across the capacitor (Vout in
the figure above) assuming the square wave input (V(t) in the figure above) is as shown
on the figure above. Sketch your prediction in the lower figure (be sure to label the
vertical scale with an appropriate numbers of volts/division). Use R = 560 Ω and C = 1
μF; show your calculations and be sure to indicate clearly what the time constant is for
this circuit. As you draw your curve, use what you learned about build-up and decay
curves in answering questions 1 and 2 to help you carefully sketch the time dependent
behavior.
Horizontal 1ms/div
Vertical 500 mV/div
Horizontal 1ms/div Vertical
6
Equipment
You will use the following equipment:
• Pasco EM-8656 AC/DC Electronics Laboratory
• Several wires of varying lengths (5, 10, and 25 cm) (in Ziploc bag)
• One each of the following resistors: 560 Ω, 100 kΩ (in Ziploc bag)
• Capacitors: one 1 μF, two 10 μF, one 100 μF (in Ziploc bag)
• Three red and three black banana plug – banana plug cables
• Four red and four black banana plug to alligator clip adapters
• Knife switch (single pole, double throw)
• BK Precision 1670A Adjustable Power Supply
• Manual range digital multimeter (DMM)
• One BNC tee (probably attached to the function generator)
• One BNC – BNC cable
• Two BNC – banana plug cables
• BK Precision 4017A Function Generator
• Tektronix TDS 1002 Oscilloscope
Since this lab involves many components, you should take a minute to see if everything
in the above list is present at your station. If you are missing something, consult with
your TA.
Activity 1: Learning the basics of the function generator and the
oscilloscope
In this part of the lab, you will go through some steps to familiarize yourself with the
operation of the oscilloscope. You will be using the Tektronix TDS 1002 oscilloscope; it
is a two channel digital oscilloscope. The oscilloscope is interfaced to the computer; you
will use this feature to print the display of the oscilloscope. You will be using the BK
PRECISION 4017A function generator to produce periodic signals. Pictures of each
device are shown below with labels to help you find the various knobs as we mention
them (see Figures 4 and 5).
7
Figure 4: Tektronix TDS 1002 two channel digital oscilloscope.
Figure 3: Tektronix TDS 1002 twFig
Figure 5: BK Precision 4017A function generator.
1. Turn on the oscilloscope and the function generator. Connect the BNC- BNC
cable to the CH1 post on the oscilloscope and to one side of the BNC ‘tee’ that
should be attached to the function generator output.
2. On the oscilloscope, press the “DEFAULT SETUP” button after the oscilloscope
has gone through its initial screens and settled on the final screen with the grid
pattern.
8
3. Set the function generator to the 100 Hz range using the appropriate frequency
range select button. Adjust the COARSE and then the FINE, FREQUENCY
knobs to set the output frequency to 100 Hz. The frequency is displayed on the
red LED display on the front of the function generator. Note: there is a delay
between when you adjust the knob and when the frequency display updates. Turn
the knobs more slowly if this delay causes you to overshoot your target frequency.
4. Select the triangle signal option among the “function selection buttons” on the
function generator. Adjust the OUTPUT LEVEL knob to about mid scale. All
the other push button settings should be in the OFF position (including the “-20
dB” button; it should be in the OFF (out) position).
5. To obtain a quick look at the signal that the function generator is producing press
the AUTO SET button on the oscilloscope. After a few seconds the oscilloscope
will display a plot of the voltage as a function of time. This plot is often called a
‘TRACE’ since the pattern is repeatedly redrawn each time the plot reaches the
end of the screen.
6. One of the limitations of the AUTO SET function is that the oscilloscope has no
way of telling what type of cable you used to connect the function generator to it.
The default setting of the oscilloscope is to assume that you are using a special
10X attenuating probe. But actually, you are using just a simple cable, so it is
important tell the oscilloscope not assume a special probe is being used. You do
this by pressing the CH1 MENU button and toggling to the 1X setting in the
Probe option (found on the right hand side of the digital display).
7. Adjust the function generator OUTPUT LEVEL knob so that the signal
displayed on the oscilloscope has a peak to peak amplitude of 10 V. The value of
the voltage will be displayed on the screen after the AUTO SET button is pressed
(under CH1 PK-PK in the lower left hand corner). (If you don’t see it, press the
AUTO SET button again.)
Question 1-1: How many vertical squares does the signal take up on the display? Since
you know that the peak to peak amplitude is 10 volts, how many volts are represented by
each major vertical division? Suggestion: you can use the POSITION knob on the
VERTICAL control panel on the oscilloscope to move the TRACE up and down for
easier measuring of the number of vertical squares.
Question 1-2: How many horizontal squares does one period of the signal take up on the
display? Since you know the period of this 100 Hz waveform, how many seconds are
represented by each major horizontal division? Hint: you can use the POSITION knob
on the HORIZONTAL control panel on the oscilloscope to move the TRACE side to
side for easier measuring of the number of horizontal squares.
9
Note: the values that you determined for the vertical and horizontal scales in Questions
1-1 and 1-2 are displayed on the bottom of the oscilloscope’s display. If the values that
you calculated for the volts/division and seconds/division above are not the same as what
are displayed, check your work.
Question 1-3: Although the AUTO SET function of the oscilloscope is useful at
initially finding the TRACE you will often need more control over how the TRACE is
displayed. To better learn how to manually set up the oscilloscope, adjust the
VOLTS/DIV knob for CH1 so that the scale is 5 volts/div. How many vertical squares
does the signal now take up on the display?
Question 1-4: Adjust the SEC/DIV knob on the HORIZONTAL control panel of the
oscilloscope so that the scale is 2.5 ms/div. How many horizontal squares does the signal
now take up on the display?
Question 1-5: Adjust the frequency push button switches and frequency control knobs on
the function generator to produce a signal of 1550 Hz. What is the period of this signal?
Question 1-6: Based on your answer to Question 1-5, what adjustment do you need to
make to the horizontal scale of the oscilloscope so you only have a few periods of the
waveform appearing in the screen? Make this adjustment and confirm that you only have
a few periods of the waveform present on the screen.
To obtain a copy of the display from the oscilloscope you will be using a program called
OpenChoice. A short cut to this program can be found in the class notes folder and on
the computer desktop. You will use this program in Question 1-7 below and other
questions to make a bitmap image of your oscilloscope screen. You will be pasting all of
your oscilloscope images into a Microsoft Word template and then printing your results
10
at the end of the lab to submit with your lab report. Open a copy of the report
template.doc document from the class notes folder and save it with a new name to the
desktop of your computer.
Question 1-7: Follow the instructions below to make a copy of the waveform (triangle
wave at 1550 Hz with only a few periods displayed) that you generated for Question 1-6
above.
Load the OpenChoice software by clicking on the shortcut and then click the “Select
Instrument” button. A menu will pop up. Choose “GPIB0::01:INSTR”. (If that choice is
not present, then look at the document Oscilloscope_bug_instructions.pdf in the
ClassNotes directory for this lab and follow the directions there.) Click on the “Screen
Capture” button and then click “Get Screen”. After the image is displayed on the
computer, click “Copy to Clipboard” to copy the image to the clipboard and then paste it
into the appropriate place in your Word template document.
Activity 2: Time Dependent Behavior of RC Circuits with Large Time
Constants
In this activity, you will observe the charge-up and decay of a capacitor in a simple RC
circuit with a large time constant. The circuit you will investigate is shown in Figure 6.
1
2
red lead
+
+
DC power
supply
CH2
black lead
_
Figure 6: Simple RC circuit with a single-pole, double-throw switch that allows a
DC power supply to be hooked up at position 1 (for charging the capacitor) or a
short circuit hooked up at position 2 (for discharging the capacitor). The voltage
across the capacitor is monitored with channel 2 of the oscilloscope. NOTE the
polarity of the electrolytic capacitor; be sure that yours is hooked up as shown. (also
see Figure 7 to understand the polarity labeling on the electrolytic capacitor).
11
Figure 7: Picture of an electrolytic capacitor similar to the ones in your bag. The
arrow pointing to the right in this picture points to the negative lead. Locate the
arrows on your capacitor. The lead they point to should be connected to the
negative (“-“) terminal of the DC power supply.
Build the circuit shown in Figure 6 using the guidance given below. Before constructing
the circuit, make sure your DC power supply is OFF. Use the 100 kΩ resistor and the
capacitor labeled 100 μF from your components bag. Before installing the resistor,
measure its resistance using the “Ω” function of the digital multimeter (DMM); make
sure to use the most sensitive scale you can. Record the measured value of the resistance
here:
R = _____________________
Use the BNC to banana plug cable to connect the oscilloscope to measure the voltage
across the capacitor (connect it to CH2 of the oscilloscope). Use the single pole, double
throw knife switch for the switch. The capacitor is an electrolytic capacitor which means
it has a polarity. Note the arrow on the capacitor; it points to the negative lead (see
Figure 7). The negative lead of the capacitor should be connected on the negative side
(“-“) of the DC power supply. (Try connecting up this circuit yourself; if you are having
trouble, you can take a look at the pictures in ph2306_lab7_circuit_examples.pdf in the
Class Notes folder).
Part 1: The capacitor charge build-up curve
Initially, leave the position of the switch not connected to either point 1 or point 2.
Question 2-1: Calculate the time constant for your circuit using the resistor value (as
measured by you) and the capacitor value (from the value written on its side). Show your
calculations below.
Before turning on your DC power supply – check that the knobs are set as follows:
Current knob should be preset at the 9 o’clock position; if you are unsure about whether it
is set correctly, ask your TA. The voltage knob should be all the way off (fully counter-
12
clockwise). Turn on the DC power supply and bring the voltage up to 10 volts (the
current should read 0.00 A).
Prediction 2-2: To set the oscilloscope to read the voltage across the capacitor as it
charges you will need to choose a vertical and horizontal scale that will fit the data you
expect. Based on the value of voltage you set on the power supply what is a reasonable
value of the vertical scale factor (VOLTS/DIV) so that the observed waveform will fill
most of the screen?
Prediction 2-3: Take a look at Figure 2 in the introduction. What is a reasonable
number of time constants to let elapse to insure that all of the interesting behavior of the
build-up is observed? Based on your calculation of the time constant in 2-1, how much
total time does this number of time constants correspond to? What value for the
horizontal scale (SEC/DIV) on the oscilloscope will be needed to display this total time?
To view Channel 2 only, press the “CH1 MENU” button until the “1” on the left hand
side of the display goes away. Then press the “CH2 MENU” button until the “2” on the
left hand side of the display is present. Look at the CH2 menu items and make sure they
are set as follows; if any of them are set incorrectly, then toggle through the options using
the button by the item of interest.
Coupling – DC
BW Limit – Off
Volts/Div - Coarse Probe – 1x
Invert - Off
Set the VOLTS/DIV knob to the value you got in 2-2 and the SEC/DIV knob to the value
you got in 2-3. For frequencies < 10 Hz the oscilloscope is automatically set to SCAN
mode and the word SCAN will appear in the top center of the display. The RUN/STOP
button will start and stop the recording of data; when data-taking is in progress the word
SCAN appears at the top of the screen; when data-taking is stopped the word STOP
appears at the top of the screen.
Press the RUN/STOP button on the oscilloscope to start recording data and set the switch
to position 1. You should see the voltage across the capacitor start to increase from 0.
Press the RUN/STOP button again to stop the recording of data when the voltage has
clearly leveled off. You will notice that the value of the maximum voltage displayed on
13
the oscilloscope is less than the 10 V you set the power supply to. (After you have done
it once, you may want to adjust things like the vertical position to get a better display. IF
you don’t like the trace you got, just hit RUN/STOP and start again).
Question 2-4: You will now use the voltage build-up curve to determine the RC time
constant. To make more accurate measurements, the oscilloscope has several useful
features. The CURSOR button places two lines on the display that can be used to make
accurate measurements. Press the CURSOR button. Press the menu button next to the
word “Source” to select CH2. Then press the menu button next to the word “Type” to
toggle through the different cursor types. One press gives two horizontal lines that can
be adjusted up and down with the VERTICAL position knobs that allow the
measurement of the voltage values. What is the final value that the voltage leveled off at
(it will not be as large as the power supply voltage) assuming it started at 0 volts?
Question 2-5: Calculate the value of the voltage that corresponds to 63% of the
maximum value. Press the menu button next to the word “Type” to toggle the cursor to
a time cursor and measure how long it took to reach this “63% of maximum” value. This
time elapsed between the two time cursors is the RC time constant; write that value
below. Capture an image of the oscilloscope screen showing the waveform and cursors
using the OpenChoice software and paste it into your Word template file.
Part 2: The capacitor charge decay curve
Now you will observe the decay in the voltage across the capacitor as it discharges
through the resistor. The switch should still be at position 1, so that the capacitor is still
fully charged. Press the RUN/STOP button on the oscilloscope to start recording data
and switch the switch position from position 1 to position 2 to let the voltage across the
capacitor decay away. Press the RUN/STOP button again to stop the recording of data
when the voltage has clearly leveled off at its final value.
Question 2-6: You will now use the voltage decay curve to determine the RC time
constant. Use the cursor function as you did previously to mark the point on your graph
where the voltage has decayed to 37% of maximum value. The time elapsed between the
two time cursors is the RC time constant. Capture an image of the oscilloscope screen
showing the cursors using the OpenChoice software and paste it into your Word template
file. Write the value of your measured time constant here.
14
Question 2-7: The capacitance of the electrolytic capacitor that you are using is marked
on its side as 100 μF. From your value of the measured RC time constant in Question 2-6
and the value of R you measured earlier, calculate the capacitance of the capacitor. Is it
within the stated manufacturer’s tolerance (you can read this off the side of the
capacitor)?
Before moving on, please TURN OFF and DISCONNECT your DC power supply.
You will not need it anymore in this lab. You can also remove the switch. But leave the
rest of the circuit (capacitor and resistor and their interconnections) in place because you
will use them in the next activity.
Activity 3: Time Dependent Behavior of RC Circuits with Short Time
Constants
You will now investigate RC circuits with smaller capacitance values. The resulting RC
time constants will be much shorter. To observe these shorter RC time constants you will
use the function generator in square wave mode. This will produce an applied voltage
V0
that will vary between some value V0 and zero:
This is equivalent to
regularly switching between position 1 and position 2 in the circuit of Figure 6 that you
used earlier in the lab. So instead of manually doing the switching, the switching is
effectively done electronically at a high rate adjustable by the function generator.
You will use your breadboard to construct the circuits for this part. Look at the circuit
shown in Figure 8. Locate the Ziploc bag with your components. Select the R = 560 Ω
resistor and the C = 1 μF capacitor. Use your DMM to measure the component’s actual
values. You can measure the resistance using the “Ω” mode in the usual way. You can
measure the capacitance by turning the knob to the “F” settings in the lower left. This
allows you to measure the capacitance of the capacitor if you plug its leads into the
rectangular holes right below the “Cx” symbol (see Figure 9); be sure to use the most
sensitive scale you can. Record your values here.
R = ___________________
C = ____________________
15
red lead
CH1
R
red lead
Function
generator
CH2
black lead
black lead
Figure 8: Simple RC circuit with a function generator operating in square wave
mode. It alternates between a voltage to charge the capacitor and zero voltage, so
the capacitor can discharge.
Figure 9: Picture of digital multimeter showing where to insert the capacitor leads to measure the
capacitance.
Question 3-1: Based on the R and C values you measured on page 15, what do you
expect the RC time constant to be for the circuit in Figure 8?
16
Construct the circuit shown in Figure 8. Use the BNC tee to connect the output of the
function generator to your circuit AND to CH1 of the oscilloscope (you use a BNC-BNC
cable from function generator to CH1 on the oscilloscope and a BNC-banana plug cable
from the function generator to the female banana plugs inputs on the circuit board). Use
a BNC to alligator clip connector to connect so that you can measure the voltage across
the capacitor; plug this in to CH2 of the oscilloscope. Also, note in Figure 8 where the
red and black leads from the BNC to banana plug cables should be located. After your
circuit is set up, turn on the function generator in square wave mode, and adjust the
function generator and the oscilloscope so that display looks like the one shown in Figure
10. To help you set up the function generator and oscilloscope correctly, answer
Questions 3-2 through 3-5 below.
Figure 10: This figure shows how the channel 1 waveform (the input signal from the
function generator) should look when you have the function generator properly
adjusted.
Question 3-2: What is the period of the square wave represented in figure 10? What
frequency should the function generator’s be output be set to, to display this frequency?
Set your function generator to this frequency.
Question 3-3: What is the peak-peak amplitude of the square wave represented in
figure 10? Set your function generator’s OUTPUT LEVEL knob to produce this
amplitude signal. Hint: you may need to push in the “-20 dB” button to get the
amplitude shown in the figure.
17
Question 3-4: What is the vertical scale factor (VOLTS/DIV) that the oscilloscope
should be set to display the square wave represented in figure 10?
Question 3-5: What is the horizontal scale factor (SEC/DIV) that the oscilloscope
should be set to display the square wave represented in figure 10?
To display both the input signal (on CH1) and the signal across the capacitor (on CH2)
you will need to turn on channel 2 of the oscilloscope. Do this by pressing the CH2
MENU button. Make sure that the “Probe” option is set to 1X.
Question 3-6: Adjust the time scale so that your display contains one complete “buildup” and decay cycle. Use the technique of the 63% point on the “build-up” curve OR the
37% point on the “decay” curve (like you did earlier in the lab). Use the cursor function
to mark on your display the points you use to calculate the RC time constant. Write the
value of your RC time constant below. Paste a copy of your display into your Word
template file. Is the result in agreement with your calculations in Question 3-1?
When you are done, please put you components back in the Ziploc bags they came in.
Please turn off the DMM meter to save the battery. Turn off your oscilloscope, function
generator, and DC power supply. Tidy up your collection of cables and connectors, so
that the work area is neat for the next pair of students. Be sure to staple your Word
document with the oscilloscope pictures to the end of this lab.
18
Post Lab questions (if there are only 10 minutes left in the lab, then skip to these
questions and complete them)
1. Below is the voltage build-up curve for an RC circuit.
a. What is the RC time constant of this circuit?
b. If the resistor in the circuit has a value of 10kΩ, what is the value of the
capacitance of the capacitor?
19
2. Below is a square waveform produced by a function generator and captured by an
oscilloscope.
a. What is the period of the waveform?
b. What is the peak-peak amplitude of the waveform?
c. What is the frequency that the function generator was set to?
20