Lab 3

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Electrical Engineering

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Jul 1, 2024

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Laboratory 2: Circuit Elements Manuelle Toro mtoromar@vols.utk.edu Purpose: For this lab we hope to put to the test our knowledge of circuits, using essential measurement such as Voltage and current, we will work with the different scenarios using the PHET Physics Circuit lab, with the use of simple circuit involving batteries and light bulbs, we will be alter several variables such as voltage and resistance, and see how different configuration affects the input of voltage to the bulbs. Finally, we hope to work with capacitors using a table of data to compare voltage to the time it takes to both charge and discharge. And as such create visible representation that helps us grasp further understanding of this concept. Activity 1 Link to the simulation: https://phet.colorado.edu/en/simulations/circuit- construction-kit-dc Click the Lab icon. Explore the interface!  Components are dragged from the toolbox to make circuits.  To explore the properties of a component, tap it. You can then change many properties and also remove the component. (a) Use one ideal battery (40 V, 0 Ω internal resistance), a light bulb (30 Ω) resistance) and ideal wires (near 0 Ω resistance) to build the circuit shown on the right. Make sure your light bulb lights up. Use the voltmeter to measure the potential difference (ΔV) across the battery. Record only the magnitude of the potential

difference (omit +/- signs). Make a similar potential difference measurement across the bulb and across each length of wire. With the noncontact ammeter, measure the current through the bulb, I Bulb . What to do if you have problems with the animation speed! Fill in "Table A" below.. ΔV Battery ΔV wire A ΔV wire B ΔV Bulb I Bulb 40 0 0 40 1.33  These results are as expected from the little variables controlled, as such given no resistance from the battery or the wire the same voltage coming from the battery should also then be present in the Light bulb Now use two ideal batteries (30 V, 0 Ω internal resistance), three light bulb (30 Ω) resistance) and as many ideal wires as needed to build several different circuits. (b) Use all the components (two batteries, 3 light bulbs) and connect them in such a way as to they produce the most light. (The largest possible current should flow through the bulbs. You can connect the batteries and bulbs in series or in parallel as needed.) Make measurements and fill in "Table B" below. Paste a screenshot of your circuit into your word document. ΔV Battery I Battery ΔV any Bulb I any Bulb 30 2.00 30 1.00

 In this circuit I was able to make it so that the voltage coming grom the battery was also present in all the bulbs and thus they shinned the most. (c) Use all the components (two batteries, 3 light bulbs) and connect them in such a way as to they produce the least amount of light or current, but not zero light or current. (The smallest possible non-zero current should flow through the bulbs.) Make measurements and fill "Table C" below. Paste a screenshot of your circuit into your word document. ΔV Battery I Battery ΔV any Bulb I any Bulb 30 0.33 10 0.33  Given this circuit, I was able to create it so that only 10 V would actually be reaching the bulbs while the battery produced 30 V Set up the circuit shown on the right with three 30 Ω bulbs and one 30 V battery.

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(d) Observe the brightness of the bulbs. Make measurements and fill in "Table D" below. ΔV Battery I Battery ΔV Bulb 1 I Bulb 1 ΔV Bulb 2 I Bulb 2 ΔV Bulb 3 I Bulb 3 30 0.67 20 0.67 10 0.33 10 0.33  Overall my observations show the bulb nearest to the battery (bulb 1) itself was the on that received the most power while both bulb 2 and 3 experience the same voltage of 10 V (e) Change the internal resistance of the battery to 2 Ω. What happens? Make measurements and fill in "Table E" below. ΔV Battery I Battery ΔV Bulb 1 I Bulb 1 ΔV Bulb 2 I Bulb 2 ΔV Bulb 3 I Bulb 3 28.72 0.64 19.15 0.64 9.57 0.32 9.57 0.32  Across the board we see the addition of resistance to the battery reduced both the Voltage of battery and bulbs as well as the current being reduced, similarly to the last case both bulb 2 and 3 changed by the same amount as well as their current. Paste Tables A - E into your log and comment on your measurements. Activity 2  Watch this Youtube video clip discussing resistors. As far as a circuit is concerned, any device that converts electrical energy into thermal energy is a resistor. But most devices have a

more descriptive name, such as hair dryer or heating element, etc. There are devices that are referred to as resistors, primary purpose is the limit the current flowing in a circuit.  Watch this Youtube video clip discussing the resistance of a light bulb. If a 9 V battery causes the same current to flow through a resistor and a light bulb, both devices dissipate the same power. But the temperature of the resistor barely changes, while the light bulb gets very hot. The resistor has a large surface area and dissipate heat efficiently by conduction and convection in air. The light bulb filament has a small surface area and is in near vacuum. It mainly dissipates heat by radiation. That only becomes efficient at high temperature, because the radiated power is proportional to thr temperature to th 4th power. ( Stefan-Boltzmann Law ).  Watch this Youtube video clip discussing diodes and LEDs. Diodes and LEDs ar semiconductor devices with conduction characteristics that can be understood using quantum mechanics but not classical theory.. In a few sentences explain how you can perform and experiment to find out if a circuit element is ohmic or nonohmic. What measurements do you make and how do you decide, based on the results of your measurements. To measure the current in a circuit, we must first connect an ammeter, a circuit element, and a variable voltage source in series. Make sure that the other components of the circuit remain constant and are properly documented to ensure proper results. We then Begin the measurement process by setting the voltage source to a low value and observing the current. Gradually we then increase the voltage supplied to the circuit element while at the same time recording the current readings at each voltage level. We must do these measurements multiple times at different voltage levels to ensure precision in our results. Next, we must construct a graph placing current on the y-axis and voltage on the x-axis. If the circuit element is ohmic, meaning it abides by Ohm's law (I = V/R), the resulting graph should display a straight line that passes through the origin. This line then shows that the resistance remains constant throughout the tested voltage range. However, if the graph exhibits a curve either upwards or downwards and is not a linear function, the circuit element may exhibit non- ohmic behavior. In this case it is implied that the resistance varies with the voltage, and does not remain constant throughout the experiment Activity 3 Charging the capacitor: With the simulation paused, start by clicking on the capacitor to discharge it. The initial voltage across the capacitor should be 0 V.

Click the start button on the stopwatch. The stopwatch will start when you play the simulation. Close switch S 1 . You will monitor the voltage across the capacitor as a function of time as the capacitor in the RC circuit is charging. Start the simulation, then pause it at roughly 0.5 V intervals between 1 V and 8.9 V and record the voltage and time in a table in this spreadsheet .  Paste a screenshot of your circuit into your word document.  Construct a plot of V c versus t and paste it into your word document. (Make sure you do not switch the axes.) o Charging the capacitor Time (s) V C (V) ln(1 - V C /9) 0 0 0 0.9 0.78 -0.09065 1.2 1.01 -0.11903 1.9 1.55 -0.18901 2.5 2.02 -0.25418 3.3 2.52 -0.3285 4.1 3 -0.40547 5 3.54 -0.49978 6 4.04 -0.59582 6.9 4.5 -0.69315 8.2 5.04 -0.82098 9.5 5.51 -0.94732 11.1 6.04 -1.11204 12.8 6.5 -1.28093 15 7 -1.50408 18.1 7.52 -1.80518 22.3 8.04 -2.23805 29.1 8.51 -2.91057 49 8.93 -4.85648 o 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 Voltage (Vc C) Time Voltage Vs Time Overall the result show that the graph that growth that increases rapidly at the beginning and then slowly reaches the 9V, this can be explained by the pushing of electron from one plate to another as the charge increases and more electrons are displaced, the lower the amount of electrons that can repel each other are present and thus the rate of charging decreased

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We expect V C = V 0 (1 - e -t/τ ), where V 0 = 9 V is the battery voltage. We can rewrite this as 1 - V C /V 0 = e -t/τ , or ln(1 - V C /V 0 ) = -t/τ. If we plot ln(1 - V C /V 0 ) versus time the slope will be -1/τ, where τ is the time constant of the RC circuit.  Add a ln(1 - V C /V 0 ) column to your spreadsheet. (The first row with the formula is already filled in.)  Plot ln(1 - V C /V O ) versus time.  Add a linear trendline, with the intercept set to zero and display the equation on the chart.  Paste it into your word document. o 0 10 20 30 40 50 60 -6 -5 -4 -3 -2 -1 0 f(x) = − 0.1 x ln(1 - VC/9) vs time Time (s) Ln (1-Vc/9)  What is your measured time constant of the RC circuit? o Given that slope is -1/τ, we can then say that -0.0996=-1/τ, as such to Find the RC we then say that τ=-1/-0.0996 giving the answer of τ=10.0402 as such RC is equal to 10.04  How does this compare to the expected time constant τ = RC? o Using the expected value determined by the formula of τ = RC we get that τ = 50x0.2 giving us a value of τ = 10, comparing this expected value to the one found using the slope of 10.04 we see the difference is insignificant, with the small difference of 0.04  How long does it take to charge the capacitor to V C = 4.5 V? o ln(1 - V C /V 0 ) = -t/τ. Using this formula we see that (Ln (1-4.5/9))x 10.04=-t, thus we get that t=6.96 seconds to reach 4.5 V Discharging the capacitor: When the capacitor is fully charged and the voltage across the capacitor is 9V, pause the simulation.

Reset and start the stopwatch. Open switch S 1 and close switch S 2 . Monitor the voltage across the capacitor as a function of time as the capacitor in the RC circuit is discharging. Start the simulation, then pause it at roughly 0.5 V intervals between 8 V and 0.1 V and record the voltage and time in the spreadsheet. Discharging the capacit Time (s) V C (V) 0 9 1.1 8.07 1.8 7.49 2.5 6.9 3.4 6.39 4.3 5.86 4.9 5.5 5.9 5.01 6 4.47 8.2 3.96 9.4 3.5 11.1 2.97 12.8 2.5 14 2.01 18.3 1.45 21.9 1.01 28.8 0.5 48.3 0.07  Construct a plot of V c versus t and paste it into your word document. (Make sure you do not switch the axes.)

o 0 1 2 3 4 5 6 7 8 9 10 0 10 20 30 40 50 60 Volatge (V) Time (s) voltage vs Time  How long does it take to discharge the capacitor to V C = 4.5 V? o The time it takes it around 6 second to go from 9V to 4.5V, based on the information from the graph and the time found in the table Reflection: To conclude this lab, I must say I found it to be quite fascinating, it’s incredible to look at the way electricity works across our entire houses and equipment and those simple circuits we believe too easy to manage and understand actually have several complex aspects that without proper practice as such used in this lab it would be unable to integrate completely into our learning path. Both the use of simple circuits using the batteries and light bulbs was quite a fun lab, additionally the final activity using capacitors and measuring the time to charge, and discharge was quite interesting, this activity is useful in allowing us to understand how charge and discharging works as this scenario plays out every single time now with the era of technology and batteries equipped on all our devices Overall the lab was quite entertaining and I hope activities like are continued to be implemented through the semester.

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