What is equivalent resistance between A and B?

A. 3R/2

B. 2R

C. R

D. R/2

To determine the equivalent resistance between points A and B, we need to analyze the configuration of the resistors in the circuit. The answer will depend on whether the resistors are arranged in series, parallel, or a combination of both. Let's break down the possibilities step by step.

Understanding Resistor Configurations

Resistors can be connected in two primary ways:

• Series Connection: In this arrangement, the total resistance (R_total) is simply the sum of the individual resistances. For example, if you have two resistors, R1 and R2, the total resistance is R_total = R1 + R2.
• Parallel Connection: Here, the total resistance is found using the formula 1/R_total = 1/R1 + 1/R2 for two resistors. This means that the total resistance is always less than the smallest individual resistor.

Example Scenario

Let's assume we have two resistors, each with a resistance of R, connected in parallel between points A and B. To find the equivalent resistance, we can apply the parallel formula:

1/R_total = 1/R + 1/R

This simplifies to:

1/R_total = 2/R

By taking the reciprocal, we find:

R_total = R/2

Evaluating the Options

Now, let's look at the options provided:

• A. 3R/2
• B. 2R
• C. R
• D. R/2

From our calculation, if the resistors are in parallel, the equivalent resistance is R/2, which matches option D. If the resistors were in series, the total would be R + R = 2R, which corresponds to option B. Therefore, the configuration of the resistors is crucial in determining the correct answer.

Final Thoughts

In summary, without knowing the exact arrangement of the resistors, we can conclude that if they are in parallel, the equivalent resistance between points A and B is R/2. If they are in series, it would be 2R. Always analyze the circuit layout to apply the correct formulas for calculating equivalent resistance.