Oscilloscope

The Tap Key

We hooked up a tap key shown above to a battery and oscilloscope. We measured the battery to have a potential of 1V. We calibrated the oscilloscope so that when the tap key was not depressed the signal on the oscilloscope was at dead center. When the tap key was pressed the line moved up one square (picture below), showing that 1V DC was going through.

The video above shows the signal jumping when the tap key was pressing. The oscilloscope was set at a slower frequency so that the "jumps" in voltage can be easily seen as the tap key was being repeatedly pressed. However, in the video, we were not still using 1V but about 1.5V. The video helps to see how the tap key interacts with the oscilloscope when there is a voltage being applied on and off.

Types of Waves

Above we can see two types of waves, a square wave and a sawtooth wave. For the square wave, the vertical lines are not visible oscilloscope as they are on the display of the function generator. There is a discontinuity in the graph. In the sawtooth wave, the wave goes from a positive slope, hits a peak and goes to a negative slope until it hits a minimum and repeats. The sine wave was completely smooth (shown in the next section below) and resembles the smooth, round, up-and-down wave that most of us are familiar with.
At 96.000 Hz, we connected a speaker to hear the various sounds of these waves. The sine wave had a low bass sound. The triangle wave had a sound that had less intensity than the previous. The square wave however was the loudest and sounded distorted. We experimented with the various controls on the function generator and found that adjusting the frequency changed the pitch of the sound produced while changing the amplitude affected the loudness of the sound produced.

Determining the Period of a Sinusoidal Wave

We connected a function generator the an oscilloscope. We set the function generation to 96.000 Hz and sine wave output. We observed the oscilloscope to have a sine wave on the screen. The oscilloscope "Time/Div" was set at 2 ms. We can compare the output of the wave from the function generator to what we see on the screen of the oscilloscope.
The function generator output a sine wave at a frequency of 96.000 Hz. We know that the period is equal to the inverse of the frequency. Therefore, the theoretical period from the function generator is T= 1/ (96.000 Hz) = 0.010.
From the oscilloscope, we measured (from where the curve first hit the x-axis to when it completed a cycle) the length of 6.5 squares. From our settings on the oscilloscope, each square is 2 ms = 0.002 s. We can compute the experimental period as follows: T = (6.5 squares)(0.002 s) = 0.013.
The percent error was 30%, however for the purpose of the experiment, we can consider it acceptable.

Observing AC and DC Quality

We connected this 6V DC transformer to the oscilloscope and observed the results. We obtained a smooth, steady straight line above 6V. Perhaps we were not calibrated at "0" before connecting the transformer. The results show a clean power source.

Here we connected the "grey" DC power source to the oscilloscope and found the source to be clean. The line was again a smooth straight line.

Here we connected an AC source and found the output on the oscilloscope to be different. Although the shape was expected, there was "noise" around the signal. This is characteristic of a "dirty" power source. The signal looks very distorted.

Lissajous Figures

We connected an AC transformer to CH1 on the oscilloscope and the function generator to CH2. Here, both inputs are being shown simultaneously. The oscilloscope was set to xy mode. This means that the input from the AC transformer will affect the x-axis while the function generator will affect the y-axis to create the Lissajous figures above.

Mystery Box

In this activity, we were given a "mystery box" that had 5 uniquely-colored terminals. The box was sealed and we cannot see the inside configuration of it. Using an oscilloscope, we were to determine the internal configuration of the box. The total number of possible configurations are 5 nCr 2 = 10 possibilities.

We went in order connecting one terminal to all other possible connections, observing the results on the oscilloscope, and then moving to another terminal until all possible 10 configurations were tested. We either obtained a voltage gain in the oscilloscope, or noise, which signified no connection between the two terminals.

The picture above shows a completed diagram showing the internal connections of the mystery box. The terminals above represent, from left to right, red, green, yellow, blue, and black. The results are that red is connected only to black. Green is connected to both blue and black. Blue is also connected to black and yellow is not connected to any terminal.

Capacitors

Charging and Discharging Capacitors

Capacitors have the ability, like batteries in a way, to hold charge. In this activity, a capacitor was charged and discharged. LoggerPro software was used to record the potential change in real time and record the data.

The graph above shows the phase when the grey power supply was used to charge the capacitor. We can see that it reaches a max of about 4.6 V and does not go higher than that. This means that the capacitor is fully charged. The behavior of potential as a function of time is given by the equation 

This graph shows the capacitor becoming discharged. We can see that it has an exponential decay. The  behavior of this process is given by the equation V=(V_0)e^(-t/RC).

Capacitance

Capacitance

In this activity, we created capacitors using two sheets of aluminum foil, separation distance (provided by sheets of paper). We carefully cut two square pieces of aluminum foil and measured the area to be 0.0316 m^2 for each. We then measured the thickness of a single page. We did this by measuring the thickness of 280 pages (making sure not to include the cover sheets and dividing the total number of pages by 2 since a single sheet has two "pages" front and back) and dividing by amount of sheets. We calculated that a single sheet measured 6.357E-2 m.

We connected a multimeter to the two sheets of foil via alligator clips. The positive end on one of the aluminum sheets and the negative end on the other aluminum sheet. We separated the two sheets of foil by a single sheet of paper and measured the capacitance with the multimeter. We did this again for 2, 10, and 15 sheets of paper and recorded the capacitance. Then we folded the aluminum sheets such that they had half of their original surface area (0.0158 m^2) and measured the capacitance again for 1, 2, 10, and 15 sheets of paper separation distance, respectively.

 When collecting data for capacitance, we pressed down on the pages so that there would be the least separation distance possible. That is, that the only separation distance is the thickness of the paper sheets, not of air or deformation in the pages which will create a higher separation distance and thus data with greater inaccuracy.

Here is the data we collected from our trials. We took this data and used excel to plot a Capacitance vs. Separation Distance graph as shown below. The blue curve corresponds to the data taken from the original foil surface area and the orange curve corresponds to half of the original surface area.

 The following observations were found to be true from the data we collected.

Resistance in Circuits

Resistance in Parallel Circuits

We were given three 150 Ω resistors and wired them in parallel. Theoretically, the total resistance should be given by the formula in blue above. The theoretical resistance of the three 150 Ω resistors in parallel is 50 Ω. We took a multimeter and measure the resistance to be 49.4 Ω which is within 1% error.

Here we analyzed a circuit where some resistors are in parallel and some are in series. We simplified the circuit in steps by combining resistors. We created a symbolic equation of the total resistance of the circuit as shown in black on the bottom right of the picture above.

Using our new skills, we created a symbolic equation for a new circuit (above). We were given the resistance of each resistor. We found that the theoretical value for the total resistance in the circuit is 52.2 Ω.

We now took the resistors and wired them up according the schematic given in the previous picture. We measured the value to be 53.6 (although it fluctuated). We subtracted the internal resistance of the multimeter, 1.4 Ω, and found that the experimental value for total resistance was the same as the calculated value.

We found that resistors add directly when they are wired in series and add in inverse when wired in parallel. We also saw that it was easier to break up a circuit into simpler circuits when trying to obtain the total resistance for the circuit.

Testing the Loop using Kirchoff's Rule

Here we applied Kirchoff's Law to find the current at different points in the circuit, across the resistors. We ended up with three equations and three unknowns for the currents. We used a matrix to solve for the individual currents (in mA). The individual values for the currents as labeled are i_1 = 1.137 mA, i_2 = 0.999 mA, i_3 = 0.138 mA.

We then set up the circuit on a breadboard as shown above. We used a potentiometer as resistor #2 and adjusted it until the resistance was 2.15 kΩ (The potentiometer was very sensitive and it was very difficult to turn it to a value of exactly 2.00 kΩ).

Next, we measured the resistance across resisors R_1, R_2, R_3, the potential differences, and currents i_1, i_2, and i_3. The data is shown in the table below.

As we can see, the % discrepancy was incredibly large (130% for the third resistor!). There is a huge source of error in the potentiometer. Therefore, we ran the experiment again, except that this time we swapped the potentiometer with a resistor that had a measured resistance of 2.13 kΩ (shown in the picture below).

We took our new measurements as shown in the table below.

We can see that our new values were much more accurate than the previous ones. The largest sources of error were in the resistors and in the battery. The battery provided 1.45 V instead of 1.50 V, and the resistors did not all match the theoretical resistances that we had used to calculate our theoretical currents.

Electric Potential

Electric Potential

In this lab, we took conductive paper that had a line and dot painted on it with metallic paint. A voltage supplier created electric potential difference between the line and dot via alligator clips. This voltage was measured as 15.02 V (please disregard the reading on multimeter as the picture was from a previous, and failed, attempt at the experiment).

We then measured two points on the higher and lower voltage, respectively. When we measured two points on the higher voltage, the reading came out to be -0.62 V. When we measured two points on the lower voltage, we got a reading of 1.37.

Starting from the point on the right, we measured the potential difference at 1 cm intervals going towards the line. We used excel to record the data and to create a  Potential vs Position graph as shown below.

Immersion Heater

Immersion Heater

In this activity we took a 3.41 W immersion heater and submerged it in a given amount of water for 10 minutes. We were to calculate how much the change in temperature of the water would be after 10 minutes had elapsed. While we performed the calculations, the water was heated and the temperature change with respect to time was tracked using LoggerPro software. At the end we compared our experimental results with the results of the LoggerPro data. The change in temperature was indeed within the uncertainty range that we had calculated.

Ohm's Law, Relating Electric Potential, Current, and Resistance

Measuring Electric Current

Here we connected a battery to power a light bulb via alligator clips. We see that all the components are functional and the bulb lights up.

We connected an ammeter to a position before and after the bulb as shown in the diagram below to measure the electric current at those positions. We found that the current was 110 +/- 5 mA for both positions. This means that the current remains constant.

Measuring Electric Potential, Current and Resistance

(Picture of the resistor used)

Our next set up was a bit different and consisted of a voltage supplier and a resistor shown in the picture below. An ammeter was again used to measure the current and a voltmeter was used to measure electric potential.

We plotted a graph showing the current vs voltage for the data that we obtained from our resistor and the data that our neighboring group obtained from their resistor. The two lines were plotted and fitted with linear trendlines which suggests that there is a linear relationship between current (I) and voltage (V), (they are proportional). We can say that I=kV, where k is a constant. We learned that solving for k (k=I/V), we get the resistance (R). So now we can say that I=RV. From our graph, the slopes of the trendlines are actually the resistance of the resistors. The two resistors were different and had a different resistance. This is shown by the slopes of the two lines, they are both different.

Other Variables

In this part of the experiment, we measured the resistance of 7 different wires with unique characteristics. They varied in material, length, and diameter. Plotting a graph of resistance vs length we get the curve shown above. The majority of the points follow a positive linear slope, however two of the points make the trendline inaccurate for this graph. We found the following relationships to hold true following our analysis.

Area (A)  is inversely proportional to the resistance (R), the wire length (L) is directly proportional to the resistance, and the resistivity of the material (rho) is directly proportional to the resistance. The data point that does not follow the trendline in the resistance vs length graph has to do with it having a larger cross sectional area (larger diameter).