The equivalent resistance between A and B is :

Solution

Physics sir · 4 steps

Name the nodes first: the crossing wires hide three equal 15 Ω paths between the same two points.

1. Spot the nodes. The horizontal middle wire jumps over the vertical wire, so the two do not touch. Call the vertical wire node P: it joins the right end of the 6 Ω, the left end of the 10 Ω, the right end of the 11 Ω and the left end of the bottom 8 Ω. Call the horizontal wire node M: it joins the bottom of the left 8 Ω, the top of the 4 Ω, the bottom of the 5 Ω and the top of the 7 Ω.
2. Three equal branches. Three separate routes go from P to M: 10 Ω then 5 Ω through the top-right corner, 11 Ω then 4 Ω through the bottom-left corner, and 8 Ω then 7 Ω through the bottom-right corner. Each route is a series pair of 15 Ω, and all three join the same two nodes, so they are in parallel.

   R_(PM) = 15/3 = 5 Ω

3. Add the series parts. From A, current goes through the 6 Ω to P, through the 5 Ω combination to M, then through the left 8 Ω to B. So R_(AB) = 6 + 5 + 8 = 19 Ω.
4. So. The equivalent resistance between A and B is 19 Ω, option (c).

The idea to keep. In a messy network, mark every point joined by plain wire as one node, then redraw. Wires that jump over each other are not connected, and equal parallel branches just divide.

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