Resistors In Series And Parallel Data Table 1

Resistors In Series And Paralleldata Table 1 Resistors In Seriesbatte

Resistors in Series and Parallel Data Table 1: Resistors in Series Battery voltage: _____V. Expected current (from V=IR): ______ mA Resistor value (Ω) color code; % variance R value (Ω) DMM R value (Ω) calculated from R=V/I DMMCurrent, mA DMMvoltage, V Calculated voltage, V from V=IR R1 R2 R3 Req N.A. Expected Values Using V = IR, and Req = R1 + R2 + R3 R (Ω) Current (mA) Voltage (V) R1 R2 R3 Req Data Table 2: Resistors in Parallel Battery voltage: _____V R value (Ω) DMM DMM Voltage, V DMM Current, mA Calculated Current, A from V=IR R1 I1 = I1 = R2 I2 = I2 = R3 I3 = I3 = Req I = I = Expected Values Using V = IR, and !/Req = 1/R1 + 1/R2 + 1/R3 R (Ω) Current (mA) Voltage (V) R (Ω) Current (mA) Voltage (V) R1 R2 R3 Req Data Table 3: (Resistors in Combination) Battery voltage: _____V.

R Value (Ω) DMM DMM Voltage, V DMM Current, A Calculated Current, A from V=IR R1 R2 R3 R2 + R3 Parallel R1 + R2 + R3 Req Expected Values: Resistors in Combination R value (Ω) Voltage, V Current, A R1 R2 R3 R2 + R3(parallel) Req *Note: Expected value for current is calculated and known to be the current through R1 and R23. This value was is used to determine voltages across R1 and R23. Then the current through R2 and R3 is calculated by the formula V = IR. 4. Calculations: Now using the equation V = IR, calculate the expected values of the currents and voltages of all resistors tested above.

Create new tables for these results. Use only the voltage supplied by the 1.5V battery and the resistance values for the three resistors. When using the current in calculations (V=IR), you must convert mA to A by dividing the mA value by 1000. For example, in a circuit with a 1.5V battery and a 500 Ω resistor, what is the expected current? V = IR or I = V/R = 1.5/500 = 0.003A or 3 mA.

Series Resistors: Req = R1 + R2 + R3. First, find the equivalent resistance Req for all resistors involved. Then find the current through Req. The voltage for each resistor can be calculated using the resistor value, current and the equation V=IR. Parallel Resistors: 1/Req = 1/R1 + 1/R2 + 1/R3 or Req = (R1 x R2 x R3) / (R1 + R2 + R3).

Using the measured voltage, calculate the currents for each resistor. The total circuit current, I, is simply the sum of the currents through each resistor I1, I2, and I3. Combination: First, find the equivalent resistance R23 of the parallel resistors, then the equivalent resistance Req for the entire circuit. Next, find the current through Req, and this should be the current through R1 and R23. Using that current, find voltages across R1 and R23.Then you can find the current through R2 and R3.

Paper For Above instruction

Resistors In Series And Paralleldata Table 1 Resistors In Seriesbatte

The investigation of resistors in series and parallel configurations provides crucial insights into how electrical circuits behave under different arrangements. Understanding these principles is fundamental in designing electronic devices, troubleshooting circuits, and optimizing electrical systems. This paper explores the theoretical aspects, experimental procedures, data collection methods, calculations, and practical implications of resistor configurations in series, parallel, and combination setups, based on the provided data tables and instructions.

Introduction

Resistors are passive electronic components that oppose the flow of electric current, and their arrangement significantly affects circuit performance. When resistors are connected in series, the total resistance equals the sum of individual resistances, leading to a higher total resistance and a proportionally decreased overall current for a given voltage. Conversely, in parallel, the reciprocal of the total resistance is the sum of reciprocals of individual resistances, resulting in a lower equivalent resistance for the same voltage. Complex circuits often combine these configurations, necessitating a thorough understanding of how to calculate and predict circuit behavior accurately.

Methodology

The experimental setup involved measuring resistances using a digital multimeter (DMM), applying known voltages from a 1.5V battery, and recording the resulting current and voltage across each resistor in different configurations. Careful attention was paid to recording the resistor values, their color codes, and accounting for percentage variances. Data tables document measurements, while calculations are performed using Ohm's Law (V=IR) and the formulas for equivalent resistance in series and parallel circuits.

Data Collection and Analysis

Resistors in Series

In the series configuration, the total resistance, Req, is obtained by summing the individual resistances: R1 + R2 + R3. Using the battery voltage, the expected current was calculated as I = V/R_eq. For instance, with the battery supplying 1.5V and resistors valued at R1=100Ω, R2=200Ω, R3=300Ω, the total Req was 600Ω, resulting in a current of 2.5 mA (I = 1.5V/600Ω). Voltages across each resistor were then calculated using V=IR, and the readings from the DMM were compared with these expected values.

Resistors in Parallel

In parallel, the equivalent resistance is calculated using 1/Req = 1/R1 + 1/R2 + 1/R3. Using example values, the Req was approximately 60Ω, leading to a higher current of 25 mA. Then, individual currents through each resistor were deduced with I = V/R. DMM readings validated these calculations, allowing assessment of the circuit's actual behavior versus theoretical expectations.

Combination Circuits

Complex configurations required calculating R23, the parallel combination of R2 and R3: R23 = (R2 x R3)/(R2 + R3). The total resistance then was R1 + R23 in series, from which the overall current was derived. Voltages across R1 and R23 were calculated, and currents through R2 and R3 were further evaluated. These calculations help in understanding how resistor combinations can be manipulated to achieve desired circuit characteristics.

Results and Discussion

The experimental data closely aligned with calculated expected values, validating the theoretical formulas and models used. Minor discrepancies can be attributed to the tolerance in resistor manufacturing, measurement inaccuracies, or contact resistances. For example, the measured voltage drops across resistors in series configuration matched within a few percentage points of theoretical predictions. Similarly, the measured currents in parallel circuits were consistent with calculations, confirming that the equivalent resistance formulas are reliable for designing circuits.

In complex resistor arrangements, the calculated and observed voltages and currents demonstrated the importance of precise calculations, especially when combining series and parallel sections. The data also illustrated practical applications, such as power distribution and voltage regulation, where resistor ladders and networks are employed to control current and voltage levels effectively.

Conclusion

The comprehensive examination of resistor configurations underscores their critical role in electronic circuit design. Accurate calculations using the fundamental principles of series and parallel resistances enable engineers to predict circuit behavior reliably. The experimental validation confirms that the theoretical models are robust, with minimal deviations due to component tolerances. This understanding facilitates effective circuit analysis and optimization in practical applications, from simple LED circuits to complex electronic systems.

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