0. The equivalent resistance between the points A and B is :

To determine the equivalent resistance between two points, A and B, in an electrical circuit, we need to analyze how the resistors are arranged—whether they are in series, parallel, or a combination of both. The method for calculating equivalent resistance varies based on this arrangement.

Understanding Series and Parallel Resistors

First, let's clarify the two main configurations:

• Series Resistors: When resistors are connected end-to-end, the total or equivalent resistance (R_eq) is simply the sum of the individual resistances. The formula is:
• R_eq = R₁ + R₂ + R₃ + ...
• Parallel Resistors: When resistors are connected across the same two points, the total resistance is found using the reciprocal formula. The equivalent resistance in parallel (R_eq) can be calculated as:
• 1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ...

Step-by-Step Calculation

Let’s walk through an example to illustrate how to find the equivalent resistance between points A and B:

• Assume we have two resistors, R₁ = 4 ohms and R₂ = 6 ohms.
• If these resistors are in series, the calculation would be:
• R_eq = R₁ + R₂ = 4 + 6 = 10 ohms.
• If they are in parallel, the calculation would be:
• 1/R_eq = 1/R₁ + 1/R₂ = 1/4 + 1/6.
• Finding a common denominator (which is 12), we get:
• 1/R_eq = 3/12 + 2/12 = 5/12.
• Thus, R_eq = 12/5 = 2.4 ohms.

Combining Series and Parallel Resistors

In many circuits, you may encounter a combination of series and parallel resistors. In such cases, it’s best to simplify the circuit step by step:

• Identify groups of resistors that are purely in series or parallel.
• Calculate the equivalent resistance for those groups first.
• Replace the group with its equivalent resistance and repeat the process until you find the total equivalent resistance between points A and B.

Practical Example

Imagine a circuit where R₁ (4 ohms) and R₂ (6 ohms) are in series with a parallel combination of R₃ (3 ohms) and R₄ (6 ohms). Here’s how you would approach it:

• First, calculate the equivalent resistance of R₃ and R₄:
• 1/R_eq3-4 = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.
• Thus, R_eq3-4 = 2 ohms.
• Now, add this to R₁ and R₂ in series:
• R_total = R₁ + R₂ + R_eq3-4 = 4 + 6 + 2 = 12 ohms.

By following these steps, you can systematically determine the equivalent resistance between any two points in a circuit. If you have a specific circuit diagram in mind, feel free to share it, and we can work through it together!