Anna Experiment 4_ Voltage Current and Resistance I

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New York University *

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Electrical Engineering

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Apr 3, 2024

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Objective: The main purpose of this experiment was to demonstrate how voltages and currents are produced, and how they are associated in resistors using Capstone with the 850 interface, a voltage sensor, an analog DC voltmeter, analog current meter, RLC circuit board, and black/red leads. If there is a voltage difference between two points, work is done by the electric field on a charge moving from one point to the other. In a circuit, each connecting wire is considered an equipotential. Earth is considered an equipotential and a water pipe is used to ground an electrical panel to limit excess charge flowing during electrical surges. Voltage is generated by batteries, signal generators, and power supplies. Voltage across a battery is DC, time independent. AC voltages are time dependent and change with time between two different points. AC voltages will repeat over an interval of time, and the time it takes to complete one cycle is called the period (T). Frequency, f or v , the number of cycles per unit time, is the inverse of the period (1/T) and is expressed in Hz when the time is measured in seconds. A waveform is the shape of the voltage vs. time graph. A voltmeter is used to measure the voltage between 2 points in an electric circuit. The 2 leads of the voltmeter are placed across a circuit on the conducting path so that the voltmeter is being connected in parallel. By connecting the voltmeter in parallel, the current is able to split and create 2 parallel circuits. A voltmeter has high resistance to ensure that it does not affect the current flowing in the circuit, and voltage (V) is measured across a resistor because it needs to be in contact with both ends of the resistor to measure the potential difference. If the leads were placed to the left or right of the resistor, the voltmeter would be in series with the resistor and no current would flow in the circuit because of its high resistance. An ideal voltmeter would not affect the voltage being measured and have no charge. Current, I, is the rate at which electric charge is passing through a point in the wire and is measured using an ammeter. The wire is broken and the two ends are connected to the ammeter. To measure the current through a resistor, the ammeter is placed in series with it so that there is only one way for the charge to flow. If current were passing through a lamp with some resistance and the lamp were taken out of the circuit and replaced with more wire, there would be more than 1 path for the current to flow and current would not be constant because the ammeter would not be in series with the wires. As more resistance is added, the total current will decrease. A resistor is a device that limits the flow of current in a circuit. The ratio of V and I across a resistor is resistance, R, which is expressed in ohms (Ω), and is a constant. Ohm’s Law, V = IR, expresses this relationship. Power of a resistor can be found using the equation P = VI, which can be rewritten as V 2 /R and I 2 R.

Two resistors connected in parallel are equivalent to a single resistor and have the same voltage across the terminals. The equivalent resistance is found using the formula: 1 𝑅𝑒? = 1 𝑅1 + 1 𝑅2 . Two resistors connected in series share the same current and are equivalent to a single resistor. The equivalent resistance is found by adding up the respective resistances: R eq = R 1 + R 2 . Procedure: The first part of the experiment focused on learning how to utilize the 850 interface to get voltage readings. Once Capstone was set up, the analog voltmeter was connected to the interface with the black and red leads. The channel and sensor were chosen on Capstone, and the auto button in the signal generator window was clicked. The waveform menu showed a DC option and 8 AC waveform options. We tinkered a bit with the controls to get used to using the equipment and set up the digits display. However, Part 5 of the experiment, which involved experiments on viewing voltages from the 850 interface, was optional. The next part of the experiment involved the RLC circuit board and observing voltage vs. current for a resistor. The resistor color code table was used to verify the resistance values of the 100 Ω and 150 Ω resistors. The analog voltmeter was removed from the output terminals of the interface and the 33 Ω resistor was connected. The signal generator was set to 0.5 V DC and 2 display windows were set up to internally measure the output voltage and output current. The resistance was calculated by dividing the voltage by the measured current. Resistance values were found for 5 more V values: 1 V, 1.5V, 2.0 V, 2.5 V, and 3.0 V. Voltage vs. current, which represents Ohm’s law, was graphed and a linear relationship was seen. Voltage and current have a directly proportional relationship.

The same process as above was repeated using the analog current meter, which was connected in series to the 33 Ω resistor. The analog current meter was set to DC 30 amps and current values were read through it. The same voltage increments and calculations were done. Comparing the values showed that the ammeter was not as precise: it increased total resistance and caused the current to drop a bit. For the last part of the experiment, AC voltages were studied as a function of time through the graph and meter displays. The 33 Ω resistor was removed, with nothing at the voltage terminals of the interface. A meter display of the output voltage was set up for 3 V AC amplitude, sine wave output, and 0.2 Hz for frequency. Because of time constrictions, only the sine waveform was examined and we observed that the meter oscillated between -1.0 to 1.0 V. Data and Calculations: 6: Carbon Resistors and the Color Code Resistor ( Ω) Color of Bands Digit/Multiplier Resistance Value ( Ω) 4th Band Color and Tolerance Range ( Ω ) Lowest Range ( Ω) Highest Range ( Ω) 100 Brown Black Brown 1 0 10 1 10 x 10 1 = 100 Gold, ±5% 100 ±5 95 105 150 Brown Green Brown 1 5 10 1 15 x 10 1 = 150 Gold, ±5% 150 ± 7.5 142.5 157.5 Sample Calculation for Range: 5% of 100 = (0.05)(100) = 5. Range = 100 ±5 = 95, 105 6.1: Discrete Measurements using Internal Measurements Output Voltage (V) Output Current (A) Resistance ( Ω) 0.499 0.00521 95.8 0.995 0.0197 50.5 1.493 0.0354 42.2 1.997 0.0506 39.5 2.493 0.0659 37.8

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2.990 0.0793 37.7 Sample Calculation for Resistance: R = = = 95.8 Ω 𝑉 𝐼 0.499 𝑉 0.00521 𝐴 6.2: Discrete Measurements using Analog Meters Sample Calculation for Resistance: R = = = 100.8 Ω 𝑉 𝐴 0.499 𝑉 0.00495 𝐴 Error Analysis: Percent Error = x 100% 𝐸𝑥?𝑒?𝑖?𝑒??𝑎? 𝑉𝑎??𝑒 − 𝑇ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒 𝑇ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒 | | | | Percent Error of Output Current Output Voltage Percent Error (%) 0.499 4.99 0.995 7.11 1.493 10.17 1.997 5.73 2.493 3.94 2.990 9.08 Sample Calculation for Percent Error: % error = x 100% = 4.99% 0.00495 − 0.00521 0.00521 | | | | Discussion: Through this experiment, we were able to successfully examine the relationship between current, voltage, and resistance. Graphing voltage vs. current showed that there is a Output Voltage (V) Output Current (A) Resistance ( Ω) 0.499 0.00495 100.8 0.995 0.0183 54.4 1.493 0.0318 46.9 1.997 0.0477 41.9 2.493 0.0633 39.4 2.990 0.0721 41.5

direct correlation between the two variables. An ideal analog current meter should have a low enough resistance so that it does not interfere with the current in the circuit. By comparing the values using internal measurements with the values using analog meters, we could see that the analog current meter is not very precise because it caused the overall resistance to be higher and the current to be lowered. The percent error for the values ranged from 3.94-10.17% and were relatively high. The discrepancy comes from the fact that our resistor is not an ideal resistor with 0 resistance.