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Experiment #17 DC Circuits Colin McCormick

Lab explores DC circuits, measuring voltage, current, and resistance. Verifies Ohm’s Law and Kirchhoff’s Rules using resistors and digital multimeters in series and parallel setups.

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    Nor11leaster i i Un ivers it y Report for Experiment #17 DC Circuits Colin McCormick Lab Partner: William Jappe and Diego Salgado Gonzalez TA: Harrison Adler February 20 th , 2024

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    Introduction In circuits powered by current, where electrically charged particles flow in a direction specific level of voltage, current and resistance are maintained. These values can be impacted by factors such as hew the circuit components are set up. However certain connections and settings are inherent to circuits with components. The goal of this lab experiment was to observe how changes in resistance, voltage and current manifest in a DC circuit. Factors like the ri'pes of resistors. How they are arranged, along with the tools for measurements, were considered during the study. Furthermore, the experiment sought to pinpoint elements within the circuit that remain constant when its layout is altered. One key aspect of rhe circuit is understanding the relationship between Resistance, Voltage, and Current of an ohmic component (an electrical component or resistor that has a constant resistance). This relationship is defined by Ohms Law as shown in Equation 1: 1: J? £ Kirchhoff's Rules are principles that govern rhe flow of currents and voltages within a circuit. These rules help in analj.'zing how voltage and current behave, in sections of a circuit and overall. The first rule, known as the Loop Rule states, that the total sum of voltage changes around a loop in a circuit is zero indicating that rhe voltages across components equal the supplied witage. Mathematically this can be represented by Equation 2 where the sum of component voltages subtracted from the supplied voltage equals zero for each resistor in rhe circuit from 1 to n. The rale, called the Junction Rule specifies that at any junction within a circuit the total sum of currents equals zero. This means that all incoming currents at a junction are distributed among branches or parallel circuits within it. This concept can be expressed by Equation 3 for each resistor from 1 to n, in the circuit. Equation 2: £ — AV 1 _ q = 0 Equation 3: J r — I 1 _ n = 0 In this lab, DC circuits w’ere assembled using a DC power source, resistors with various nominal resistances, and Digital Multimeters (DMMs). The purpose of incorporating DMMs was to accurately measure voltage, current, or resistance at various segments within rhe constructed circuits. Each segment with known resistance or witage was checked using a DMM to confirm its actual value. DMMs where used to measure voltage and current at different parts of the circuit to verify Ohm's Law and Kirchhoffs Rules. This process ensured the generation of currents and voltages that aligned with the expectations for resistors arranged either in parallel or series, contingent upon the circuit configuration. Additionally, it was verified that the inclusion of DMMs in the circuits had a negligible impact on their functionality while a steady voltage was maintained.

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    Investigation 1 Investigation 1 was conducted to study the voltages in a circuit with two batteries and understand how the DMM functions in series. The voltages across each battery were measured in both directions. From positive to terminals and vice versa. It was noted that the voltage magnitude remained consistent in both directions only changing its sign (see Table 1 for values). This finding supports the idea that current represents the movement of charged particles through the terminals with a reversal in direction when the terminals are switched. After measuring each battery's voltage, a circuit was set up with the batteries connected in series along with a voltmeter. Figure 1 shows the schematic of this series circuit with the batteries. The voltmeter readings indicated that the total circuit voltage (with batteries in series) was approximately equal to the sum of both battery voltages (refer to Table 1 for values). The next step involved rearranging the batteries into a configuration as shown in Figure 2. In this arrangement the voltmeter displayed a circuit voltage, to that of a batten 7 alone (see Table 1 for exact values). In both the series and parallel setups, the voltages measured marched the expected voltages of the circuit closely with very little percent error. Figure 1: Batteries in series Figure 2: Batteries in parallel Table 1: Voltages Across Investigation 1 Circuits Voltage (V) Expected Voltage % Error BT1 1.4798 1.5 1 346667 BT2 1.4092 1.5 6.053333333 Series 2.886 2.889 0.10384216 Parallel 1.4519 1.4445 0.512287909 The results of Investigation 1 showed that w p hen batteries are connected in series their ’s’oltages add up while, in a setup the overall voltage is similar to that of each batten;. This finding was backed by the percent error values in the majority of the data collected. Any small discrepancies in measurements could be due to the batteries being left unused for periods, possibly causing discharges over time.

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