1. To: Anders Ask
Name: Tyler Mooney
Course Title: MA100B Introductory Course in Mathematics and Physics
Assignment: Lab Exercise part 3 and part 4
Date: 2 February 2016
3. 3
Task 1
I. Theoretical Data
For this task, the goal is the successfully read and measure different signals from a function generator
using an oscilloscope and test how the different control knobs affect the image on the oscilloscope. The
measurements are used from a coaxial cable outputting from the function generator and inputing into the
oscilloscope. On the oscilloscope, a picture is generated showing what the function generator is doing.
For part one of the task we are to output Sinusoidal signal with amplitude 7.0V, offset 0V and frequency
2kHz from the function generator. Part two of this task is to create a square wave with amplitude 6.0V
and symmetric around 3.0V and frequency 10kHz.
II. Test Results
Part one:
Part two:
III. Test Result Explanation
For part A of this task the seven control knobs we used are the following:
VOLTS/DIV: This allows us to get a better understanding of the voltage outputted by the signal, if you
have a high voltage signal, you should increase your voltage.
4. 4
TIME/DIV: This shows the time period of the signal. If you have a high frequency signal you should have
a lower Time/Div setting.
NM/AT: Moves the signal from fallen edge to rising edge or vice versa.
LEVEL: Used to move the signal from left to right, changing the starting/ending point
SLOPE: Changes the signal from positive to negative or vice versa
TRIG. CHI and CHII: Triggers between the signals channel 1 and channel 2. If pressed it shows both
channels.
INV. CHII: When pressed it gave me a flat signal, when held down it allowed me to see the continuation
of my signal
For part B of the task we tested the following control knobs:
AC/DC: When DC is pressed, it shows us both the AC and DC offset of the signal.
GD: The ground button shows us where the signal is 0V on the oscilloscope.
IV. Conclusion
In conclusion we were able to gain a better understanding of what the knobs do to effect the output signal
from the function generator. Also with the knobs we are able to gain more precise and accurate reading.
5. 5
Task 3
I. Theoretical Data
The goal of this task is to find the inductance (L) over four different coils by measure the time constant
(tau). A diagram is given for the connection and the inductance used for each measurement is L1= 1200
without the core, L2 = 1200 with open core, L3 = 1200 with closed core L4 = 600 with closed core. The
frequency will be chosen so that the image can be deduced on the oscilloscope.
II. Test Results
L1:
L2:
τ = 5x10-5
s
6. 6
L3:
L4:
III. Test Result Explanation
Using the image we are able to calculate the inductance from L1 by using the formula tau = L/R. The
formula is then changed to L = tau x R. Plugging in the numbers we received from the oscilloscope we
then found the inductance by calculating L = 5x10-5
x 1000, which equals 0.05H (henrys).
7. 7
Other results:
L τ x R L(H)
L1 5x(10^-5) x 1000 0.05
L2 3.5x(10^-4) x 1000 0.35
L3 1.8x(10^-3) x 1000 1.8
L4 5x(10^-4) x 1000 0.5
IV. Conclusion
In conclusion the resistor and the core effect the size of L. A larger resistor will reduce the value of L,
and the size of the coil also effects the value for L. The magnetic flux also effects the size of the
inductance.
8. 8
Task 4
I. Theoretical Data
For this task we are to examine the relationship between the period and the time constant (tau) and how it
affects the output signal. A diagram is given to set up the connection with a resistor (R) size 1kΩ and a
core capacitor (C) with the size 20nF. The input signal from the function generator should be a square
wave with amplitude 4.0V and symmetric around 2.0V.
II. Test Results
Period >> τ τ = 2.2x10^-3s or
2.2ms
Period ≈ τ τ = 2.2x10^-4 or
220µs
Period << τ τ = 2.2x10^-5 or
22µs
9. 9
III. Test Result Explanation
With this image we were able to calculate tau. The formula for this is tau = RC. With our numbers the
final calculation is tau = 10000 x 2.3x10-8
, which the final answer for this is tau = 2.3 x 10-4
(s).
IV. Conclusion
In conclusion it can be seen that tau is very similar to the period of the graph. The core capacitor also has
an effect on the graph similar to the resistor.
63% = τ = 220µs
10. 10
Task 5
I. Theoretical Data
The goal of this task is to measure the voltmeter values and compare them with theoretical data. The
oscilloscope is used as a reference tool, and the power must be measured in AC. The readings must vary
between 20Hz and 20kHz. The oscilloscope graph should be a sinusoidal with an amplitude of 6.0V
offset 0.0V. The purpose of the task was to test at what frequency our Vrms would be out of range as we
change the frequency from 20Hz to 20kHz. The Vrms value we should be aiming for is around 4.24V. To
calculate our Vrms we used the formula:
Vrms= V(max)/ (Vmax=6).
II. Test Results
frequency (Hz)
oscilloscope
(V) voltmeter (V)
20Hz 6.0V 4.07V
200Hz 6.0V 4.05V
2kHz 6.0V 4.05V
20kHz 6.0V 5.41V
III. Test Results Explanation
The voltage value of the oscilloscope never changes, because we use it as a reference for the amplitude of
the signal. When testing the voltmeter voltage, we realized that once we decrease our frequency to around
19Hz our voltmeter got a reading that didn’t match out Vrms, and once we increased it to 20kHz it also
was out of the limit.
11. 11
IV. Conclusion
In conclusion, the limit Vrms, of a sinusoidal signal with an amplitude of 6V ranges anywhere from 20Hz
until 19.8kHz.
12. 12
Task 6
I. Theoretical Data
For this task the goal is to measure the voltage across a voltmeter with different frequencies, as well as the
capacitor resistance. Then the next part of the task is to measure the phase shift between the voltage and
the current, using an oscilloscope. Channel 1 measures voltage across the resistor and channel 2 measures
the output voltage of the function generator. Another point of this is to see how the capacitor acts as a
resistor in AC current.
II. Test Results
frequency Vc I Vc/I Xc = (1/2πfC)
200Hz 1.355V 1.777x(10^-3)A 762.72Ω 795.775Ω
400Hz 1.058V 2.748x(10^-3)A 385.05Ω 397.887Ω
1000Hz 0.6508V 4.0887x(10^-3)A 146.74Ω 159.155Ω
200Hz:
400Hz:
1000Hz:
13. 13
TIME/DIV frequency measured Ø = arctan(xc/R)
1mS 200Hz 1.0134rads 1.178rads
1mS 400Hz 0.89rads 0.878rads
200µS 1000Hz 0.436rads 0.449rads
III. Test Results Explanation
For the first part we calculated the capacitor resistance using the formula Xc = (1/2πꝭC) this gave us the
theoretical value of our capacitor resistance. In order to get our measured values, we used the formula
Vc/I. We calculate Vc with a voltmeter and the I with the equation I=V/R were V is our signal amplitude
and R is the resistance of the resistor plus the capacitor. With Vc and I calculated we proceeded to
calculate our measured capacitor resistance, which was very similar to our theoretical values. For part 2
we were supposed to measure the phase shift of our signal. In order to do this, we used the formula Ø =
arctan(xc/R) which gave us a theoretical value. Our measured values were calculated by counting the
spaces between 1 period of the signal using the oscilloscope . Once we obtained the number of spaces I
used the formula 2π/#spaces, which gives us the value in radians of each space. In order to calculate the
phase shift, we then manually counted the spaces between the 2 signals and multiplied that by value in
radians of each space.
IV. Conclusion
In conclusion, the frequency of a sin signal, with an AC current, has a direct impact with the resistance of
a capacitor, affecting the phase shift and the voltage over a capacitor
