Final answer:
The correct option is B. To find the equivalent resistance between points A and B', we can simplify the circuit. By combining resistors in parallel, the equivalent resistance is found to be R.
Step-by-step explanation:
To find the equivalent resistance between points A and B', we can simplify the circuit using a series of steps. First, we notice that the combination of R and 2R is in parallel with 3R. We can simplify this by combining R and 2R into a single resistor, which would have a resistance of 3R/2.
Now, we have two resistors in parallel: 3R/2 and 3R. The formula for calculating the total resistance of two resistors in parallel is 1/R_total = 1/R1 + 1/R2. Applying this formula, we get 1/R_total = 1/(3R/2) + 1/(3R). Simplifying, we get 1/R_total = 2/3R + 1/3R = 3/3R = 1/R. Taking the reciprocal of both sides, we find that the equivalent resistance is simply R. Therefore, the correct answer is B) R.