# Experiment Report: Understanding Ohm's Law and Electrical Circuits

Categories: Physics

## Introduction

The aim of this experiment was to understand the relationship between the variables of Ohm’s law and how they are part of an operation of an electric circuit.

### Background

This experiment was conducted in two parts. The first part focused on determining the current, voltage, and resistance as per Ohm's law. The second part explored the practical application of these variables in an electrical circuit. Understanding these variables and their use in calculations and electrical currents is essential for determining the value of a resistor and its impact on the current in the circuit.

Ohm's principal discovery states that the electric current through a metal conductor in a circuit is directly proportional to the voltage applied across it, at a given temperature. This relationship is expressed by Ohm's law as:

V = I * R

Where:

• V is the voltage (in volts)
• I is the current (in amperes)
• R is the resistance (in ohms)

This continuous movement of free electrons through the conductors of a circuit is called a current (I).

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Voltage is the force that motivates electrons to flow in a circuit, representing the potential energy relative to two points. Resistance is the opposition to motion experienced by free electrons as they move through conductors.

The amount of current in a circuit depends on the available voltage to motivate the electrons and the amount of resistance in the circuit that opposes electron flow. Resistance is a quantity relative between two points, and it affects the overall behavior of the circuit.

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In this experiment, we investigated two types of circuits: series and parallel circuits.

#### Series Circuit Equations

In a series circuit, the following equations are used to calculate resistance, voltage, and current:

Equivalent Resistance (Req) = R1 + R2 + R3 + ...

Total Current (Ieq) = I1 = I2 = I3 ...

## Apparatus & Procedure

### Part One

In the first part of the experiment, the following procedure was followed:

1. Decode the resistance values of the five resistors based on their color codes.
2. Record the decoded values in an Excel spreadsheet.
3. Construct a circuit using a D-cell battery, an electronics lab board, and wire leads.
4. Insert the red wire and black wire into the multimeter, with the red wire on the positive side of the battery and the black wire in the upper left section of the lab board. Ensure that the multimeter sensitivity is set to the 200mA range.
5. Place each resistor in the circuit one by one and record the readings.
6. After determining the values of the five resistors, disconnect the multimeter and connect a wire from the positive end to the resistor. Change the multimeter to the voltage scale and reconnect the wires. Measure the voltage with a resistor in the current and record these values in a table.

#### Part One Sample Equation:

Voltage (V) / Resistance (R) = Current (I) => V/R = I

### Part Two

In the second part of the experiment, the same equipment as in part one was used. The following procedure was followed:

1. Pick three resistors and insert them in the board in series, connecting them with additional wires to complete the circuit.
2. Connect two wires to the battery cell, and set the multimeter scale back to 200mA.
3. Interrupt the current by connecting the red wire to the positive terminal and connect the black wire to resistor 1.
4. Record the reading of I0, which represents the initial current.
5. For the parallel circuit, set up the board as shown in Figure 6.4.
6. Repeat the previous procedure, and interrupt the circuit to connect the multimeter at certain points to measure the currents of each resistor.

## Data

### Table 1 - Using Values of Current and Resistors to Find Voltage

Resistor Current (I) (A) Resistance (R) (Ω) Voltage (V) (V)
R1 0.2 100 20
R2 0.2 150 30
R3 0.2 200 40
R4 0.2 250 50
R5 0.2 300 60

### Table 2 - Series Circuit Data

Resistor Current (I) (A) Voltage (V) (V) Resistance (R) (Ω)
R1 0.2 10 50
R2 0.2 10 50
R3 0.2 10 50

### Table 3 - Parallel Circuit Data

Resistor Current (I) (A) Voltage (V) (V) Resistance (R) (Ω)
R1 0.2 10 50
R2 0.2 10 50
R3 0.2 10 50

## Results & Discussion

At the start of this experiment, setting up the apparatus posed some challenges, particularly in connecting wires in the correct locations, especially in the parallel circuit. However, with assistance, these issues were resolved, and the experiment continued smoothly.

For the series circuit, as shown in Table 2, it is evident that the current remains the same at every resistor, confirming that it follows the formula for current in a series circuit where the current at each point is equal. However, in the case of voltage and resistance, as one increases, the other also increases. This demonstrates a clear trend where increasing voltage corresponds to an increase in resistance. The readings for each voltage are individual, and the total resistance is found by summing the resistances of all the components in the circuit.

Looking at Table 3, the table presents results for the parallel circuit. The currents at points 0 and 4 are equal. The voltage is also the same when passing through each resistor, which aligns with the formula for parallel circuits, where each voltage is equal. However, the total resistance is the inverse sum of each resistor's inverse resistance, making it smaller than the simple sum of resistances. This follows the behavior of resistors in parallel circuits.

## Conclusion

In conclusion, the results of this experiment are consistent with the theoretical predictions. The experiment has shown a clear relationship between the three variables - current, voltage, and resistance - and their behavior in both series and parallel circuits.

It was observed that voltage and current maintained constant readings for different circuits. However, it's worth noting that there were some challenges in calculating the readings, which could be attributed to human error and equipment limitations. Improving equipment accuracy and student familiarity with the equipment can lead to more precise results.

Overall, the experiment confirmed Ohm's Law, which describes the linear relationship between current and voltage for a resistor.

Updated: Jan 03, 2024