Total Equivalent Resistance

Oct 13, 2025 by wbrum.org 120 views

Introduction

In this article, we will explore the concept of resistances connected in series and parallel configurations. We will analyze the circuit shown in the figure and determine the potential difference between points Vp and Vq. This problem requires a deep understanding of the properties of resistances and how they behave when connected in different configurations.

Understanding the Circuit

The circuit consists of six resistances, each with a value of 6 ohms. The resistances are connected in a combination of series and parallel configurations. To determine the potential difference between points Vp and Vq, we need to analyze the circuit and identify the equivalent resistance between these two points.

Equivalent Resistance

The equivalent resistance between points Vp and Vq can be determined by analyzing the circuit in sections. We can start by identifying the resistances that are connected in series and then determine the equivalent resistance for each section.

Series Resistances

The resistances R1, R2, and R3 are connected in series. The equivalent resistance for this section can be calculated using the formula:

R_eq = R1 + R2 + R3

Substituting the values, we get:

R_eq = 6 + 6 + 6 R_eq = 18 ohms

Parallel Resistances

The resistances R4, R5, and R6 are connected in parallel. The equivalent resistance for this section can be calculated using the formula:

1/R_eq = 1/R4 + 1/R5 + 1/R6

Substituting the values, we get:

1/R_eq = 1/6 + 1/6 + 1/6 1/R_eq = 3/6 R_eq = 2 ohms

Total Equivalent Resistance

The total equivalent resistance between points Vp and Vq can be determined by combining the equivalent resistances of the series and parallel sections.

R_total = R_eq_series + R_eq_parallel R_total = 18 + 2 R_total = 20 ohms

Potential Difference

The potential difference between points Vp and Vq can be determined using Ohm's law:

V = IR

where V is the potential difference, I is the current flowing through the circuit, and R is the total equivalent resistance.

However, we do not have the value of the current flowing through the circuit. To determine the potential difference, we need to analyze the circuit further.

Current Flow

The current flowing through the circuit can be determined by analyzing the circuit in sections. We can start by identifying the current flowing through the series section (R1, R2, and R3).

I_series = V/R_eq_series I_series = V/18

The current flowing through the parallel section (R4, R5, and R6) can be determined using the formula:

I_parallel = V/R_eq_parallel I_parallel = V/2

Total Current

The total current flowing through the circuit can be determined by combining the currents flowing through the series and parallel sections.

I_total = I_series + I_parallel I_total = V/18 + V/2

Simplifying the expression, we get:

I_total = (V/18) + (9V/18) I_total = 10V/18 I_total = V/1.8

Potential Difference

Now that we have the total current flowing through the circuit, we can determine the potential difference between points Vp and Vq using Ohm's law:

V = IR V = (V/1.8) * 20 V = 20V/1.8 V = 11.11V

Conclusion

In this article, we analyzed the circuit shown in the figure and determined the potential difference between points Vp and Vq. We used the properties of resistances and Ohm's law to calculate the equivalent resistance and potential difference. The potential difference between points Vp and Vq is 11.11V.

References

[1] Ohm's Law
[2] Resistances in Series and Parallel Configurations
[3] Equivalent Resistance

Q&A

Q: What is the equivalent resistance between points Vp and Vq?

A: The equivalent resistance between points Vp and Vq can be determined by analyzing the circuit in sections. We can start by identifying the resistances that are connected in series and then determine the equivalent resistance for each section.

Q: How do we calculate the equivalent resistance for the series section?

A: The equivalent resistance for the series section can be calculated using the formula:

R_eq = R1 + R2 + R3

Substituting the values, we get:

R_eq = 6 + 6 + 6 R_eq = 18 ohms

Q: How do we calculate the equivalent resistance for the parallel section?

A: The equivalent resistance for the parallel section can be calculated using the formula:

1/R_eq = 1/R4 + 1/R5 + 1/R6

Substituting the values, we get:

1/R_eq = 1/6 + 1/6 + 1/6 1/R_eq = 3/6 R_eq = 2 ohms

Q: What is the total equivalent resistance between points Vp and Vq?

A: The total equivalent resistance between points Vp and Vq can be determined by combining the equivalent resistances of the series and parallel sections.

R_total = R_eq_series + R_eq_parallel R_total = 18 + 2 R_total = 20 ohms

Q: How do we determine the potential difference between points Vp and Vq?

A: The potential difference between points Vp and Vq can be determined using Ohm's law:

V = IR

However, we do not have the value of the current flowing through the circuit. To determine the potential difference, we need to analyze the circuit further.

Q: How do we calculate the current flowing through the circuit?

A: The current flowing through the circuit can be determined by analyzing the circuit in sections. We can start by identifying the current flowing through the series section (R1, R2, and R3).

I_series = V/R_eq_series I_series = V/18

The current flowing through the parallel section (R4, R5, and R6) can be determined using the formula:

I_parallel = V/R_eq_parallel I_parallel = V/2

Q: What is the total current flowing through the circuit?

A: The total current flowing through the circuit can be determined by combining the currents flowing through the series and parallel sections.

I_total = I_series + I_parallel I_total = V/18 + V/2

Simplifying the expression, we get:

I_total = (V/18) + (9V/18) I_total = 10V/18 I_total = V/1.8

Q: What is the potential difference between points Vp and Vq?

A: Now that we have the total current flowing through the circuit, we can determine the potential difference between points Vp and Vq using Ohm's law:

V = IR V = (V/1.8) * 20 V = 20V/1.8 V = 11.11V

Frequently Asked Questions

What is the equivalent resistance between points Vp and Vq?
- The equivalent resistance between points Vp and Vq is 20 ohms.
How do we calculate the equivalent resistance for the series section?
- The equivalent resistance for the series section can be calculated using the formula: R_eq = R1 + R2 + R3
How do we calculate the equivalent resistance for the parallel section?
- The equivalent resistance for the parallel section can be calculated using the formula: 1/R_eq = 1/R4 + 1/R5 + 1/R6
What is the total equivalent resistance between points Vp and Vq?
- The total equivalent resistance between points Vp and Vq is 20 ohms.
How do we determine the potential difference between points Vp and Vq?
- The potential difference between points Vp and Vq can be determined using Ohm's law: V = IR

Conclusion

References

[1] Ohm's Law
[2] Resistances in Series and Parallel Configurations
[3] Equivalent Resistance