The equivalent resistance between A and B is _________.

Solution

Physics sir · 3 steps

Both side wires are plain wire, so every corner is A or B. Then it is just branches in parallel.

1. Merge the corners. The left vertical line has no resistor, so both left corners are at the potential of A. In the same way, both right corners are at B. The two diagonals meet at a centre point C.
2. Read the branches. The 8 Ω and 2 Ω both join A to C, and the 4 Ω and 6 Ω both join C to B. Every other resistor path runs straight from A to B.

   Branch from A to B	Resistance
   Top: 1.5 Ω and 0.5 Ω in series	2 Ω
   Upper horizontal	12 Ω
   Through C: (8 ∥ 2) + (4 ∥ 6) = 1.6 + 2.4	4 Ω
   Lower horizontal	6 Ω
   Bottom: 1 Ω and 1 Ω in series	2 Ω

   1/R_(AB) = 1/2+1/12+1/4+1/6+1/2 = (6+1+3+2+6)/12 = 3/2 Ω⁻¹

3. So. R_(AB) = 2/3 Ω, which is option (b).

The idea to keep. Before using any formula, collapse every plain wire into a single node. Most scary-looking networks then turn into simple branches in parallel between the two terminals.

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