Equivalent Resistance Calculation:

To find the equivalent resistance between points A and E, we need to analyze the given circuit and identify the resistors connected in series and parallel.

Step 1: Identifying Resistors in Series and Parallel:

The circuit consists of four resistors (R) connected in a specific arrangement. Let's analyze the circuit and identify the resistors connected in series and parallel.

1. Resistors R1 and R2 are connected in series as they share a common current path. The current passing through R1 is the same as the current passing through R2.

2. Similarly, resistors R3 and R4 are connected in series.

3. The combination of resistors R1 and R2 is connected in parallel with the combination of resistors R3 and R4.

Step 2: Calculating Equivalent Resistance:

Now that we have identified the resistors connected in series and parallel, we can calculate the equivalent resistance step by step.

1. Equivalent resistance of resistors R1 and R2 in series (Rs1):
Rs1 = R1 + R2

2. Equivalent resistance of resistors R3 and R4 in series (Rs2):
Rs2 = R3 + R4

3. Equivalent resistance of the combined series resistors (Rs):
Rs = Rs1 + Rs2

4. Equivalent resistance of the parallel combination (Rp):
1/Rp = 1/Rs1 + 1/Rs2

To simplify the calculation, we can use the formula for two resistors in parallel:
1/Rp = 1/Rs1 + 1/Rs2 = (Rs1 + Rs2) / (Rs1 * Rs2)

Now, rearranging the equation, we get:
Rp = (Rs1 * Rs2) / (Rs1 + Rs2)

5. Finally, the equivalent resistance between points A and E (Req):
Req = Rs + Rp

Substituting the values of Rs and Rp calculated above, we get:
Req = Rs + (Rs1 * Rs2) / (Rs1 + Rs2)

Simplifying further, we can express Req in terms of R:
Req = 2R + (R/2) = 5R/2

Conclusion:

The equivalent resistance between points A and E is 5R/2.