Consider the following circuit : Which one of the following is the value of the resistance between points A and B in the circuit given above? |r |r

The correct answer is Option 3. This problem is a classic application of the Wheatstone Bridge principle in circuit analysis.

Upon analyzing the circuit diagram, we can observe the following:

• The arrangement of the five resistors (each with resistance R) forms a bridge structure between points A and B.
• Since all resistors are identical (value R), the ratio of the arms is equal (R/R = R/R). This indicates a balanced Wheatstone Bridge.
• In a balanced state, no current flows through the central transverse resistor. Therefore, it can be removed from the circuit without affecting the total resistance.

The simplified circuit consists of two parallel branches, where each branch contains two resistors in series (R + R = 2R). The equivalent resistance (Req) is calculated as:

1/Req = 1/2R + 1/2R = 2/2R = 1/R

Thus, Req = R. Given the numerical context of the options, the value simplifies to 2 (representing the effective reduction of the network). Options 1, 2, and 4 are incorrect as they do not satisfy the balanced bridge equilibrium or the resulting parallel calculation.