Question

The equivalent resistance of the circuit shown in the figure between points A and B is:

• A. \(1\,\Omega\)
• B. \(0.5\,\Omega\)
• C. \(2\,\Omega\)
• D. \(4\,\Omega\)

Hint:

In symmetric resistor networks, always check for zero current in central branches due to equal potential points.

Answer 1

The Correct Option is A

Step 1: Circuit symmetry.
The network is symmetric about the vertical midline, placing symmetric nodes at equal potential.

Step 2: Balanced bridge elimination.
The central vertical 2 Ω resistor carries no current and can be removed.

Step 3: Simplifying upper branches.
Each side becomes series 2+2 = 4 Ω; these two 4 Ω branches are in parallel, yielding 2 Ω.

Step 4: Including the bottom resistor.
The bottom 2 Ω resistor is directly across A and B, parallel to the upper 2 Ω.

Step 5: Final parallel combination.
2 Ω ∥ 2 Ω = 1 Ω.

Step 6: Conclusion.
Equivalent resistance between A and B is 1 Ω.