Lab Report: Verification of Ohm's Law

Abstract

The objective of this lab was to confirm Ohm's law by investigating the relationship between electrical current, voltage, and resistance. The experiment also explored current flow and voltage in both series and parallel circuits. Additionally, the lab determined the equivalent resistance for series and parallel combinations of resistors and compared the results with theoretical values.

Introduction

Ohm's law states that the electric current (I) through a conductor is directly proportional to the voltage (V) across it and inversely proportional to the resistance (R) of the conductor.

Mathematically, Ohm's law is expressed as:

I = V / R

The unit of current is the ampere (A), and the unit of resistance is the ohm (Ω). In this lab, we aimed to verify Ohm's law by conducting experiments that involve varying voltage and resistance while measuring the resulting current.

We used ammeters to measure current and voltmeters to measure voltage. These devices allowed us to create and measure electrical circuits. The key components of our experiments were the variable resistor box and power supply.

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In the second part of the lab, we explored resistors connected in series and parallel. The total resistance in a series circuit is the sum of the individual resistances, while in a parallel circuit, it involves the reciprocal of the sum of the reciprocals of the individual resistances.

Materials and Methods

The following equipment and materials were used in the experiment:

• Variable resistor box
• Ammeter
• Voltmeter
• Power supply
• Resistor box

Experimental Procedure

Part 1: Verification of Ohm's Law

1. Investigate the variation of current with potential difference (voltage) when resistance is constant:
   1. Set up the circuit as shown in Figure 4.
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      2 with a constant resistance of 1000 Ω.

   2. Adjust the ammeter to the mA range and the voltmeter to the 25V range.
   3. Turn on the power supply.
   4. Vary the output voltage of the power supply from 4 V to 10 V in 1 V increments and record the voltage (V) and corresponding current (I) in Table 1.
   5. Repeat the same procedure with a resistance of 1200 Ω.
2. Investigate the variation of current with resistance when voltage is constant:
   1. Use the same circuit setup with a constant output voltage of 12V.
   2. Vary the resistance of the resistor box from 700 Ω to 1700 Ω in 200 Ω increments while keeping the voltage constant.
   3. Record the current (I) and corresponding resistance (R) in Table 2.

Results

The data collected during the experiment is presented in the following tables:

Table 1: Variation of Current with Potential Difference (Voltage)

Table 2: Variation of Current with Resistance

Calculations

Calculations

Part 1:

1. Use the data from Table 1 to plot a graph of current (I) vs. voltage (V) for both values of resistance (1000 Ω and 1200 Ω).
2. Determine the slope of the graph. From the slope of the graph, find the resistance using the formula:
   • a) For 1000 Ω resistance: R = V / I
   • b) For 1200 Ω resistance: R = V/ I
3. Calculate the percent difference for each resistance value using the formula:

[% diff] = |R_theoretical - R_experimental| / R_theoretical * 100%

Discussion

Question 1:

Does your resistance follow Ohm's law? Base your answer on your experimental data.

The resistance closely follows Ohm's law because when we analyze the data mathematically, it is closely related to the resistance values present in the data. The percent difference calculations also support this conclusion, as the values are close to zero, indicating good agreement between experimental and theoretical resistance values.

Question 2:

A typical color television draws about 2.5 A when connected to a 120V source. What is the effective resistance of the TV set?

To find the effective resistance (R_TV) of the TV set, we can use Ohm's law:

I = V / R_TV

Given that I = 2.5 A and V = 120 V, we can rearrange the formula to find R_TV:

R_TV = V / I = 120 V / 2.5 A = 48 Ω

The effective resistance of the TV set is 48 Ω.

Question 3:

Explain the difference between series and parallel connections.

In a series connection of resistors, the total resistance is the sum of the individual resistances. Mathematically, it is represented as:

R_total = R₁ + R₂ + R₃ + ...

On the other hand, in a parallel connection of resistors, the total resistance is determined by taking the reciprocal of the sum of the reciprocals of the individual resistances. Mathematically, it is represented as:

1 / R_parallel = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...

Question 4:

Does your experiment present evidence that the current divides in a parallel circuit?

No, our experiment did not present evidence of current division in a parallel circuit. In a parallel circuit, the total current is equal to the sum of the currents through each individual branch. However, in our experiment, we did not investigate current division in a parallel circuit.

Question 5:

From your experimental observations of a series circuit, what relationship do you find between the voltages across the individual resistances and the voltage across the entire series group?

In a series circuit, the voltage across each individual resistor adds up to equal the total voltage across the entire series group. Therefore, the relationship is that the voltage across the individual resistances (V₁, V₂, V₃, etc.) is equal to the voltage across the entire series group (V_total). Mathematically, it can be expressed as:

V_total = V₁ + V₂ + V₃ + ...

Question 6:

From your experimental observations of a series circuit, what relationship do you find between the voltages across the individual resistances and the current flow across the entire series network?

In a series circuit, the current flow (I) is the same through each individual resistor as it is across the entire series network. Therefore, the relationship is that the current flowing through the individual resistors (I₁, I₂, I₃, etc.) is equal to the current flowing across the entire series network (I_total). Mathematically, it can be expressed as:

I_total = I₁ + I₂ + I₃ + ...

Conclusion

The results of both parts of this lab experiment demonstrated the relationship outlined by Ohm's Law. The direct relationships between voltage, current, and resistance were clearly observed. The experiments allowed us to measure voltage and current without prior knowledge of resistance. Additionally, by manipulating voltage and resistance, we systematically collected data that provided a practical illustration of Ohm's law.

The experiment also highlighted the difference between resistors connected in series and those connected in parallel. In series, the total resistance is the sum of individual resistances, while in parallel, it involves the reciprocal of the sum of the reciprocals of the individual resistances.

Recommendations

For future experiments in this area, it is important to ensure the accuracy of measurements and to minimize sources of error. Additionally, exploring more complex circuits and practical applications of Ohm's law could provide further insights into electrical behavior and circuit analysis.