DC circuits

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Northeastern University *

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1146

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Electrical Engineering

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Apr 3, 2024

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Report for Experiment #17 DC circuits Introduction: In this lab simple electric circuits are studied and examined closely. Electric circuits work as they have a flow of current moving through them, current can be described as the flow rate of charge past a certain point per unit of time. The following equation describes this relationship:

I = ΔQ / Δt (17.1) Apart from these circuits are varying amounts of resistance (resistance to charge flow) and voltage potential (electrical tension due to varying amount of charge). To create an electric circuit a close wire loop must be attached to opposing sides of a current source/battery as charge flow is a result of opposing voltage values due to the opposite terminal of charges in the battery source. A battery that is not however in a closed loop maintains an electromotive force (emf) due to the voltage difference between two terminals, this value is constant in this case. This value of emf describes the amount of work done to charge in moving charges from one terminal to another, the following equation shows this relationship: ε = ΔW / Δq (17.1) Resistance to the flow of charge as mentioned briefly is properly known as resistance (R), and it can be described as the ratio between the change in voltage and current. This ratio is known as ohm's law where volts/amp is measured in ohms (Ω). Lastly the amount of energy/ time or work per unit time a circuit does is known as the power of the circuit, using ohm's law it can be further simplified to obtain new relationships. The following equations describe these relationships: P = ΔW / Δt = I 2 R (17.4) There are rules that govern the currents and voltages that run a circuit, and they are Kirchhoff's rules. The first one, the loop rule, dictates that the sum of all voltage differences in a closed circuit is zero. The second rule, the junction rule, dictates that the sum of all currents flowing into a junction must be zero, in other words what goes in must come out. The goal of this lab along with understanding the elements of a circuit is to measure currents, and voltages using digital multimeters and apply kirchhoff's rules of circuits to analyze and test different circuits. In investigation 1 the voltage across batteries in parallel and in series and alone are measured to understand voltage differences due to the combinations. In investigation 2 ohmic resistance is thoroughly analyzed and ohm's law is applied to calculate resistance and internal resistance is found. In investigation 3 two resistors in series and in parallel are studied as kirchoff's rule are applied and the current and power for both circuits are experimentally found. Studying these fundamental rules is crucial to understanding circuits, this is important as all electronics function in some shape or form due to circuits. Investigation 1: Electromotive force of Battery combinations To begin this investigation first the DMMs device was inspected thoroughly, next the voltage across a single battery was measured using the device. The DMM was connected as a voltmeter across the battery and cables were used to attach the positive battery end to the terminal and the negative end to the other negative terminal. The proceeding voltage measurement was then recorded on excel, next two batteries were attached to each other in series and the voltage once again measured and recorded separately. Lastly the batteries were connected in parallel using more cables, and the voltage across this circuit was measured and recorded.

Data table for investigation 1: V one battery voltage 1.324 one battery voltage 1.554 two battery voltage series 2.887 two battery voltage Parallel 1.437 Investigation 2: Ohmic resistance To begin this investigation the DMM was set to an ohmmeter to measure and record resistance. Using a circuit element box for resistors the 100 ohm resistor was measured using the ohmmeter, the actual value for resistance for this resistor was recorded on excel and the value was within tolerance. Next the emf of one of the batteries was measured, this battery was used for the rest of the investigation. A circuit was then made to measure the current through the 100 ohm resistor connected in series with the battery. To do so one of the DMMs was set up to be an ammeter, and the current was measured and recorded. Next the second DMM was added to the circuit and set as a voltmeter to measure the voltage across the resistor. From the values of current and voltage that were measured using ohm's law the experimental value for resistance was calculated. Next the voltmeter was disconnected and re attached to measure the voltage across current meter to get the value for burden on voltage. Lastly the results from this investigation was used along with equation ΔV source = ε − I ∗ r (17.13) to find the internal resistance, r, of the battery. These values were recorded in excel. Data table for investigation 2: emf V 1.34 resistance 100.29 I (mA) 13.303 V( with R) 1.325 Calc R value 99.60159363 V without R 14.5

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(mV) r 2.307692308 R amp 1.076923077 Investigation 3: Simple resistor networks In this investigation first two resistors are set up series to each other and studied. The resistors used were on the circuit element box and they were the 470 ohm and 1000ohm resistors. First a ohm meter was used to check and record the actual resistances of these labeled resistors on the element box. As in investigation 1 the power supply voltage was measured, and the PS was turned on and set to a voltage of 5v, then the DMM after being used to measure voltage was disconnected. Then both resistors were set up in series using the cables provided and attached to the PS. One DMM was used to measure the current in the circuit and the voltages were also measured across every circuit element with the second DMM. The voltage drops over all the circuit elements were summed and compared to the measured value of the supply voltage (5V) and using equation (17.4) P = ΔW / Δt = I 2 R the power was calculated. Next resistance was calculated using ohm's law and compared to the measurements made for each resistor using the DMM. For the second part of this investigation the exact same steps were followed however this time it was for a circuit where both resistors are in parallel no in series. Resistance and power were calculated in the same fashion as the first half of this investigation for this new circuit and record in excel. Data table for investigation 3: Two resistors in series: Actual (O) V 470 ohms 487.7 1.1668 1000 ohms 975.3 3.337 Current meter 0.322 current amp (A) 0.0032 Sum of voltage drops 4.8258

Power 470 (A) 0.002791516 Power 1000 (A) 0.011417583 Exp R 1000 1042.8125 Exp R 470 417.9808022 Two resistors in parallel: I (A) V 470 487.7 0.0125 4.98 1000 975.3 0.0046 4.98 current meter (V) 0.001646 Exp R 1000 1082.608696 Exp R 470 398.4 current meter (A) 0.01534 Power 1000 0.022908 Power 470 0.06225 Conclusion: The goal of this experiment was to understand circuits and elements of circuits via applying kirchhoff's rules and ohm's law. In investigation 1 the voltage was found across one batter and two batteries in series combination and in parallel. In investigation 2 ohmic resistance was measured using a single battery and this value was then calculated experimentally using ohm's law and internal resistance of the battery was found in order to study resistance in a circuit. Lastly in investigation 3 two combinations of resistor circuits were made, one with two in parallel and another with two in series. For both combinations using ohm's law experimental resistance was found and compared to the theoretical DMM measured values and the power was also found for the circuits. In investigation 1 the series voltage (2.887 V) was approximately equal to the the sum of both individual voltages of each battery, the voltage in parallel however dropped and remained about the same as one battery which makes sense considering that in parallel the voltage experienced by each section is equal to the original voltage of one power source. In the circuit where the batteries are in parallel the current value is being increased while the voltage output is the same and for in series as observed the voltage in increased and current remains the same, optimal for an electric powered scooter perhaps. In investigation 2 the calculated R value of 99 ohms approximately matches the theoretical 100.29 ohms resistance that

was measured, thus proving ohm's law. In investigation 3 the current measurement for the resistors in parallel are 0.01534 A which is larger than the value for current for the resistors in series which is .0032 A. This value is expected as in parallel you increase the current as the voltage experienced by each resistor is the same and in series the voltage experienced by each resistor is not the same. Lastly the power values calculated for each resistor in parallel which were 0.22908W for the 1000ohm resistor and .06225 W for the 470 ohms resistor. These values were larger than the values for power for each resistor in series which were .002792 W for the 470 ohm resistor and .011 W for the 1000 ohm resistor. They were expected to be larger because for resistors in parallel there is much less resistance than in series thus charge flow is not as interrupted. This experiment could have been improved by as error is attributed to faultiness of the cables and error by the DMM’s. Questions: 1. The terminal voltage available is 4.5V 2. Resistance is greater in series as there are less paths the charges flowing through the circuit can take, while in parallel the increase in paths decrease the resistance. The new resistance in series will be double the ohmic resistance of one, while in parallel it will be equal to 1 R eq = 1 R 1 + 1 R 2 . 3. 1.5 V .2 A = 7.5 Ohms 4. The resistance of a 1.5Kw/110V electric tea pot is 110 2 1500 W = 8.1 Ohms 5. A ¿ 1 − 1 2 R = r B ¿ 1 − 1 2 R + 1 − 1 2 R = 2 r References: ● Introductory physics lab textbook ● Anh Nguyen

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