In the given circuit, the equivalent resistance between the terminal A and B is __________ Ω.

Solution

Physics sir · 4 steps

Spot the bare wire joining top and bottom on the right: it shorts out everything beyond it.

1. Find the short. Just right of the second 2 Ω vertical resistor, a plain wire joins the top rail to the bottom rail. The two ends of that wire are at the same potential, so no current enters any resistor sitting between those two points.
2. Drop shorted parts. The right vertical 2 Ω and the 4 Ω + 4 Ω loop both connect the top rail to the bottom rail across that wire. Both are shorted, so they carry no current. The top 2 Ω now runs straight from the left junction down to the bottom rail.
3. Middle section. Between the left junctions there are now two 2 Ω paths in parallel: the left vertical one, and the top 2 Ω that returns through the shorting wire. Together they give (2 × 2)/(2 + 2) = 1 Ω.

   R_(AB) = 3 + 1 + 6 = 10 Ω

4. So. The 3 Ω and the 6 Ω are in series with this 1 Ω, so the equivalent resistance between A and B is 10 Ω.

The idea to keep. Before you combine anything, hunt for wires that join two rails directly. Every resistor lying between the two ends of such a wire is shorted and drops out of the calculation.

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