Lab Report 3 Expirement 17.docx (1)

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Report for Experiment #17 DC- Circuits Gabriela Martinez Lab Partner: Paige TA: October 10, 2023

Introduction Numerous circuits powering everyday household devices rely on a direct current (DC) circuit, where charged particles flow consistently in one direction. This transfer of DC current is facilitated by converting chemical energy into electrical energy. For current to flow effectively, batteries universally feature two conductive terminals. To denote polarity, the positive terminal is consistently labeled with a "+" sign. A charged battery not coonecte to a circuit maintans a constant voltage difference called the electromotive force (emf) between its terminals is defined as the ratio of work done to ϵ ∆? charge in moving from the negative to the positive terminal. ∆? ∆? ϵ = ∆? ∆? The dimension of is thus work/charge, which in units is Joule/Coulomb, a unit also called ϵ Volt(V). The current I is defined as the charge Q that flows per unit time t in a circut. 𝐼 = ∆? ∆? Electric current is quantified in Coulombs per second, known as the Ampere (A). Another crucial parameter of a battery is its capacity to deliver a total charge, denoted as Q. The device referred to as a "variable voltage supply" utilized in this experiment essentially functions as an advanced battery. It upholds a constant DC voltage disparity between two terminals and derives its energy from an AC (alternating current) electrical outlet. The electromotive force (emf) of this supply can be configured and fine-tuned by manipulating a dial or knob. A power supply is characterized by the maximum voltage and the maximu current it can deliver. The ration of voltage/current supplies to a circut is called resistance. Higher resistance means less current flow. When a positive current flows from the + terminal, through a circut element, to the - terminal . it starts out at a higher potential and end up at a lower potential. Thus theres is a voltage drop across the element.,. If a current I flows through the circut element, the ∆? resistance R of the element can be defined as ? = ∆? 𝐼 The unit of R is Volt/Ampere, which is given the name Ohm . R is is constant over a wide Ω range of currents. The Ohms law is known as the voltage drop acrosa resistor is proportional tot he current. Power P (energy/time) or work per unit of time delivered in a circut element. ∆?/∆? Units are Watt (W).

? = ∆? ∆? = ∆?𝐼 = ∆? 2 ? = 𝐼 2 ? This lab consisted of 3 investigation centered around DC circuits and their characteristics. The primary objective was to validate or refute Kirchhoff's rules pertaining to loops and junctions, which delineate how circuit components operate when arranged in series or parallel configurations. The initial investigation focused on examining the electromotive force of batteries, both individually and in series or parallel arrangements. This entailed a comparative analysis of electric potential sources in parallel and series configurations. The second investigation delved into Ohmic resistance, with the aim of substantiating Ohm's law. This was achieved by determining a resistor's actual resistance using an ohmmeter, and subsequently contrasting it with the calculated resistance derived from measurements of current and voltage. The third investigation revolved around resistor networks, specifically comparing resistors organized in series with those in parallel. The total resistance determined in the series arrangement was juxtaposed with two calculated resistance values based on Ohm's law, accounting for total voltage and total current in the context of parallel resistors. Additionally, this value was compared with that derived from Kirchhoff's junction rule for resistors in parallel. . Investigation 1 To start this investigation, commence by measuring the voltage of a single battery. Ensure that the DMM is configured to measure voltage by pressing the DC V button. Subsequently, establish a connection between the DMM, set up as a voltmeter, and the battery. Use a patch cable to link the positive + battery terminal to the DMM's positive (red) V input, and another patch cable to connect the negative - battery terminal to the DMM's negative COMM input. Refer to the circuit diagram below for guidance. Document the voltage recorded by the DMM in an Excel sheet; this value represents the electromotive force (emf) of the battery. The error for was 1% of the calculated Voltage. Reverse the lead connections and conduct the measurement once more. Repeat this process for the second battery.

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Alignment Voltage of Battery 1 Error Voltage of Battery 2 Error Correct way 1.6 0.016 1.4 0.014 Reverse -1.6 0.016 -1.4 0.014 After completing the voltage measurements for both batteries, proceed to connect them in series as depicted below. Repeat the previous steps and document the voltage across the combined batteries. It's evident that the measurements deviate from the assumption of the meter's 1% precision.The error for was 1% of the calculated Voltage. Voltage of batteries in series Error 3.08 0.308 To conclude the investigation, join the two batteries in a parallel arrangement, as illustrated in the circuit diagram provided below. Gauge and document the voltage across the combination, specifically between one positive terminal and one negative terminal.The error for was 1% of the calculated Voltage. This measurement aligns with the initial reading obtained in the first step, demonstrating the same voltage. Voltage of batteries in parallel Error 1.6 0.016 In a flashlight, batteries are often arranged in series, stacked one atop the other. This configuration boosts the voltage supplied to the flashlight, resulting in a brighter illumination. On the other hand, in a remote control, batteries are typically arranged in parallel, positioned

next to each other. This setup extends the operational duration of the remote, as it consumes energy at a slower rate. . Investigation 2 To start the next investigation we need to disconnect the battery and use the DMM as an ohmeter to measure and record the actual value of the 100 resistor in the circuit box. The error for was 1% of the Ω calculated measurement. The results werent within nominal tolerance meaning the two values were inconsistent. Measurement of 100 ohm resistor Error 109.7 1.097 Next we measured and recorded the emf of one battery and used that recording from here on. The error for was 1% of the calculated measurement. emf of one battery Error 1.6 0.016 The subsequent step involved constructing a circuit for gauging the current passing through the 100 resistors arranged in a series configuration with the battery, following the provided circuit diagram. One of the DMMs will be configured to function as an ammeter. The two current terminals will be designated for 20 A maximum and the other for a lower current of 500 mA. Connect the red terminal labeled "500mA max input" and the black terminal marked "COMM" and select the DC current measurement. Once the setup is complete, proceed to measure and document the current.The error for was 1% of the calculated measurement. I (mA) error 14.25 0.1425 Adding the second DMM to our circut as a voltmeter, we measured the voltage across the the resistor. Leaving the first DMM in the circut as is. The voltage across the resistor is shown below. The error for

was 1% of the calculated measurement. The set up of the circut can also bee seen below in the circuit diagram. voltage across resistor (V) error 1.56 0.0156 We were then told to calculate the resistor value from the previous step and compare it with the measurement from step 1. To calculate the resistor value we used the equation below. The error equation can also be seen below. ? = ? 𝐼 δ? = ? ( δ? ? ) 2 + ( δ𝐼 𝐼 ) 2 calculated resistor value (V/mA) error 0.109473684 0.001548192 The computed resistor value aligns with its measured resistance, as the disparity is within twice its margin of error. Subsequently, without disassembling the remainder of the circuit, detach the voltmeter from its placement across the resistor and employ it to gauge the voltage across the current meter. Although this voltage may be modest, it is not insignificant. Document this measurement; what we have just assessed is known as the burden voltage.The error for was 1% of the calculated measurement. Burden Voltage(V) Error 0.0168 0.000168

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During the second phase of this inquiry, we assessed the open circuit voltage of the battery. Moving forward, the third phase involved measuring the current. In steps 4 and 6, we took readings of the voltages across the resistor and ammeter. These values serve as the basis for determining the battery voltage under a load , .With these results and the equation below ∆? ?????? we can find the resistance of the battery. ∆? = ϵ − 𝐼? (V) ∆? ?????? Error 1.5768 0.015600905 Ir (ohms) error 7.587592982 0.130958 Investigation 3 Two resistors in Series To begin this investigation we used the DMM as an ohmeter to check and record the actual rsitances of the resistors. These are the measured resistances we will be using in the calculations from 470Ω 𝑎?? 1𝑘Ω here on. The error for was 1% of the calculated measurement. Actual resistance of 470(OHM) error actual resistance of 100k error 495 4.95 1019 10.19 With the power supply switched off, establish a connection to the DMM to ascertain the voltage supplied, akin to previous experiments. Ensure that the DMM is configured for DC voltage measurement. Proceed to power on the PS and adjust the voltage to 5V. Utilize the DMM to gauge the supply voltage. Once the PS is configured, power it down without altering the settings, and then detach the DMM. Linking the two resistors sequentially to the power supply (PS), employ one of the DMMs to gauge the circuit's current. Upon activating the PS, proceed to measure and document the voltage readings across each element in the circuit using the second DMM. In order to achieve this, we

will relocate the connection points of the second DMM to three distinct circuit positions.A diagram of the circut can be seen below. Upon completion of the measurements, power down the PS. The error for was 1% of the calculated measurement. V for R1 error V for R2 error V for current meter (V) error V3 Amps (A) error 1.63 0.0163 3.4 0.034 0.001 0.00001 0.0034 0.000034 After we finished measuring we summed all the voltage drops over all the circut elements. The error for the voltage drop can be found using the equation below. δ∆? = ∆? (δ? 1 ) 2 + (δ? 2 ) 2 + (δ? 3 ) 2 V ∆ error 5.031 0.03770531 Next we found the power dissipated in each resistor using the equation below. The equation for the error can also be seen below ? = ∆? 2 ? = 𝐼 2 ? δ? = ? (2 δ𝐼 𝐼 ) 2 + ( δ? ? ) 2

Power R1 (W) error Power R2 (W) error 0.005367475 7.64443E-05 0.011344455 0.000162 We cross-referenced the total resistance obtained in the initial step with the value calculated using Ohm's law, as defined in the equation below, employing the measurements from the third step. The associated error equation is also provided below. Notably, these two measurements demonstrate consistency, given that their disparity is within twice the margin of error. Not factoring in the burden voltage didn't introduce any complications for these measurements; in fact, it led to more accurate results that closely approached the theoretical value. ? = ∆? 𝐼 δ? = ? ( δ∆? ∆? ) 2 + ( δ𝐼 𝐼 ) 2 Ohms Law - R error 1479.705882 489.63834 Two resistors in Parallel The DMM was used to set the power supply to 5V once more, after which it was turned off. Following this, we proceeded to connect the same pair of resistors in parallel with the power supply. One DMM was employed to gauge the overall current, while the second DMM was utilized to document the voltages across all three components in the circuit. Additionally, we measured the individual currents flowing through each of the resistors. The circuit diagram illustrating all these measurements is presented below. The error for was 1% of the calculated measurement.

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Total current (A) 0.0149 error 0.00149 V for R1 4.99 error 0.0499 V for R2 4.99 error 0.0499 V for Ampmeter 0.00027 error 0.0000027 Current through R1 (amps) 0.01 error 0.001 Currrent through 2R (amps) 0.0048 error 0.000048 R1 (ohms) 499 error 0.1004988

R2 (ohms) 1039.5833 error 0.0141421 Power R1 (W) 0.0499 error 0.000706 Power R2 (W) 0.023952 error 0.000339 To calculate the total resistance of resistors in parallel, we used the equation below: 1 ? = 1 ? 1 + 1 ? 2 The error is the same a previously calculated. The theoretical resistance was by using Ohms Law. The error was found with the equation below. δ? = ? ( δ∆? ∆? ) 2 + ( δ𝐼 𝐼 ) 2 The measured resistance value aligns with the theoretical value, confirming conformity with the parallel resistor addition rule. However, upon examining the recorded current output from the power supply, it becomes evident from the table that it does not correspond with the currents passing through the individual resistors. The process of determining power dissipation and its associated error followed the same methodology as that for resistors in series. It is apparent that the power dissipated in parallel configurations surpasses that in series. This is attributed to the fact that the resistance (R) in parallel circuits is lower than that in series circuits. Consequently, the power dissipation in parallel circuits surpasses that in series circuits. The power equation is provided below for reference ? = ∆? 2 ? Conclusion In this experiment, currents and voltages in simple circuits were better understood by making measurements with digital multimeters and construction from circut diagrams. In the first investigations the emd for each batter was and with error being 1% of ϵ 1 = 1. 6? ϵ 2 = 1. 4? the results. When measuring the voltage across connected in series, V. For the ϵ = 3. 08 ± 3. 08

batteries connected in parallel V. Both were consistent with their rules for voltage in ϵ = 1. 6 ±. 016 parallel and series. In the second investigation, we found that measured values of EMF current and voltage, the internal resistance of the battery was ohms. 7. 587592982 ± 0. 130958 The third investigation revolved around resistor networks, specifically comparing resistors organized in series with those in parallel. The total resistance determined in the series arrangement was juxtaposed with two calculated resistance values based on Ohm's law, accounting for total voltage and total current in the context of parallel resistors. Additionally, this value was compared with that derived from Kirchhoff's junction rule for resistors in parallel. Questions 1. A 6 V battery is connected in series with a 1.5 V flashlight cell. What possible terminal voltages are available? 7.5V 2. You are given two equal resistors. Will the total resistance be larger when they are in series or parallel? What will the new resistance be in each case? The total resistance is larger when they are series, the resistance is 2R for series and for parallel its ( 1 ? 1 + 1 ? 2 ) −1 3. Does a 1.5 V battery have an internal resistance? If the maximum current the battery can supply is 200 mA, what is the value of its internal resistance? yes, 7.5 homs 4. What is the resistance of a 1.5 kW/110 V electric teapot? R= 8.07 ohms 5. Determine the resistance between points A and B in Figs. 17.8a and 17.8b, where the dotted lines indicate that the visible circuit pattern is repeated infinitely to the right. A) the resistance is zero B) the resistance is 2R

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References IPL manual https://macmillan.vitalsource.com/reader/books/9781533950932/epubcfi/6/250[%3Bvnd.vst.idref%3Dv st-451ef310-4ad4-4378-bdb7-6d07db982599]!/4