Understanding Series and Parallel Resistances

Oct 13, 2025 by wbrum.org 103 views

Introduction

In this problem, we are given five equal resistances of 10 Ω connected between points A and B. The question asks us to find the resultant resistance between these two points. To solve this problem, we need to understand the concept of series and parallel resistances.

Understanding Series and Parallel Resistances

When resistances are connected in series, the total resistance is the sum of the individual resistances. On the other hand, when resistances are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

Analyzing the Given Circuit

In the given circuit, the five equal resistances of 10 Ω are connected between points A and B. To find the resultant resistance, we need to analyze the circuit and determine whether the resistances are connected in series or parallel.

Breaking Down the Circuit

Let's break down the circuit into smaller sections. We can see that there are two parallel branches, each consisting of two resistances of 10 Ω. These two branches are connected in series, and the resultant resistance of each branch is 5 Ω (since 2 x 10 Ω = 20 Ω, and 20 Ω / 4 = 5 Ω).

Finding the Resultant Resistance

Now that we have found the resultant resistance of each branch, we can find the total resultant resistance of the circuit. Since the two branches are connected in series, the total resultant resistance is the sum of the resultant resistances of each branch, which is 5 Ω + 5 Ω = 10 Ω.

Conclusion

In conclusion, the resultant resistance between points A and B is 10 Ω. This is because the five equal resistances of 10 Ω are connected in a way that they form two parallel branches, each with a resultant resistance of 5 Ω, and these two branches are connected in series.

Final Answer

The final answer is a) 10 Ω.

Additional Information

It's worth noting that the other options, b) 5 Ω, c) 15 Ω, and d) 6 Ω, are not correct. Option b) 5 Ω is incorrect because the resultant resistance of each branch is 5 Ω, but the total resultant resistance of the circuit is 10 Ω. Option c) 15 Ω is incorrect because the resultant resistance of each branch is 5 Ω, and the total resultant resistance of the circuit is 10 Ω, not 15 Ω. Option d) 6 Ω is incorrect because the resultant resistance of each branch is 5 Ω, and the total resultant resistance of the circuit is 10 Ω, not 6 Ω.

Key Takeaways

When resistances are connected in series, the total resistance is the sum of the individual resistances.
When resistances are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.
The resultant resistance of a circuit can be found by analyzing the circuit and determining whether the resistances are connected in series or parallel.
The total resultant resistance of a circuit is the sum of the resultant resistances of each branch, if the branches are connected in series.

Frequently Asked Questions

What is the resultant resistance of a circuit with five equal resistances of 10 Ω connected between points A and B?
How do we find the resultant resistance of a circuit with resistances connected in series and parallel?
What is the difference between series and parallel resistances?

References

[1] "Circuit Analysis" by Charles K. Alexander and Matthew N. O. Sadiku
[2] "Electric Circuits" by James W. Nilsson and Susan A. Riedel
[3] "The Art of Electronics" by Paul Horowitz and Winfield Hill

Introduction

In our previous article, we discussed the problem of five equal resistances of 10 Ω connected between points A and B. We found that the resultant resistance between these two points is 10 Ω. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q1: What is the resultant resistance of a circuit with five equal resistances of 10 Ω connected between points A and B?

A1: The resultant resistance of a circuit with five equal resistances of 10 Ω connected between points A and B is 10 Ω.

Q2: How do we find the resultant resistance of a circuit with resistances connected in series and parallel?

A2: To find the resultant resistance of a circuit with resistances connected in series and parallel, we need to analyze the circuit and determine whether the resistances are connected in series or parallel. If the resistances are connected in series, the total resistance is the sum of the individual resistances. If the resistances are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

Q3: What is the difference between series and parallel resistances?

A3: The main difference between series and parallel resistances is the way they are connected. In series resistances, the current flows through each resistance in sequence, and the total resistance is the sum of the individual resistances. In parallel resistances, the current flows through each resistance simultaneously, and the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

Q4: Can you explain the concept of equivalent resistance?

A4: Yes, the equivalent resistance of a circuit is the total resistance of the circuit, which is the sum of the individual resistances if they are connected in series, or the reciprocal of the sum of the reciprocals of the individual resistances if they are connected in parallel.

Q5: How do we calculate the equivalent resistance of a circuit with multiple branches?

A5: To calculate the equivalent resistance of a circuit with multiple branches, we need to analyze the circuit and determine whether the branches are connected in series or parallel. If the branches are connected in series, we can calculate the equivalent resistance by summing the individual resistances. If the branches are connected in parallel, we can calculate the equivalent resistance by taking the reciprocal of the sum of the reciprocals of the individual resistances.

Q6: What is the significance of equivalent resistance in circuit analysis?

A6: The equivalent resistance of a circuit is significant in circuit analysis because it allows us to simplify complex circuits and analyze their behavior more easily. By finding the equivalent resistance of a circuit, we can determine the total resistance of the circuit and analyze its behavior under different conditions.