The equivalent resistance of the given circuit between the terminals A and B is :

Solution

Physics sir · 4 steps

Spot the bare wire on the left first: it shorts the 5 Ω, then fold the ladder up from the left towards A.

1. The short. The bare wire on the far left joins the top and bottom rails. So the left end of the top rail is at the same potential as B, and the 5 Ω has no voltage across it. No current flows through it, so remove it.
2. Fold from left. Call the junction above the middle 2 Ω point M. From M there are two paths down to the bottom rail. One is the top 2 Ω going left, then the short wire. The other is the vertical 2 Ω. These are in parallel, so M to bottom is (2 × 2)/(2 + 2) = 1 Ω.
3. Add the series part. The second top 2 Ω runs from A to M. It is in series with that 1 Ω, so this branch gives 2 + 1 = 3 Ω from A to B.

   1/R_(AB) = 1/3 + 1/3 + 1/3 = 1

4. So. That 3 Ω branch sits between A and B together with the two vertical 3 Ω resistors. All three are in parallel, so R_(AB) = 1 Ω, which is option (d).

The idea to keep. In a ladder, first look for any bare wire across two rails. Remove the resistors it shorts, then combine from the end farthest from the terminals and work back towards them.

Answer from the NTA final answer key. Solution by PrepWiser.