In the given figure, `R = 3Omega`. Determine equivalent
resistance between points A and B.
.

Options

A. `3 Omega`
B. `2 Omega`
C. `15 Omega`
D. `6 Omega`

Answer

B

Explanation

b. Step 1: Attach a 100 V battery and assign potential at each node.

Step 2: By symmetry `100 - y = y -0 or y = 50V`
Step 3: Now apply KCL at node c
`(x-100)/R + (x+50)/R + (x-0)/R = 0 `
` or x = 50 V`
Step 4: If `R_(eq)` is equivalent resistance of this circuit, we have
`100/R_(eq) = x/R + 50/R + 50/12 or R_(eq) 2/3 R`
Alternative method
Making 2D projection
There is perpendicular axis of symmetry, i.e., the points COP
will be equipotential then the circuit will be
rArr 2/3 R` .