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

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Index

Task 1…………………………………………………………………………………………………3-4

Task 3…………………………………………………………………………………………………5-7

Task 4…………………………………………………………………………………………………8-9

Task 5…………………………………………………………………………………………………10-11

Task 6…………………………………………………………………………………………………12-13

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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.

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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.

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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 = 5x10-5s

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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).

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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.

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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

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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

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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.

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IV. Conclusion

In conclusion, the limit Vrms, of a sinusoidal signal with an amplitude of 6V ranges anywhere from 20Hz

until 19.8kHz.

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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:

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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