The equivalent resistance between A and B is . [Figure: a rectangle whose left side is a plain wire (node A) and right side is a plain wire (node B). Top edge: 12 Ω from A to B. Bottom edge: 6 Ω from A to B. Above the rectangle, a triangle path from the top-left corner through 1.5 Ω and then 0.5 Ω…

Question

The equivalent resistance between A and B is . [Figure: a rectangle whose left side is a plain wire (node A) and right side is a plain wire (node B). Top edge: 12 Ω from A to B. Bottom edge: 6 Ω from A to B. Above the rectangle, a triangle path from the top-left corner through 1.5 Ω and then 0.5 Ω to the top-right corner. Below it, a triangle path from the bottom-left corner through 1 Ω and 1 Ω to the bottom-right corner. Two diagonals cross and are joined at the centre node O: 8 Ω and 2 Ω from the left corners to O, 4 Ω and 6 Ω from O to the right corners.]

Accepted Answer

(1) 2/3 Ω. The left side is a plain wire, so both left corners are A; likewise both right corners are B. Top triangle: 1.5+0.5=2 Ω; bottom triangle: 1+1=2 Ω; edges 12 Ω and 6 Ω; all from A to B. Diagonals: 8∥2=1.6 Ω from A to O, 4∥6=2.4 Ω from O to B, total 4 Ω. 1/R=1/2+1/(12)+1/4+1/6+1/2=3/2 R_AB=2/3 Ω

Step-by-step solution

Why the other options are wrong