In the above arrangement, each side of the cube has 1   Ω resistance and it is known that the effective resistance between A and B is 5 9   Ω . Now, if the resistor between A and B is removed, then find the new effective resistance (in Ω ) between the same two points.

Step-by-step solution

i. For a cube of resistors each of resistance R the equivalent resistance between two edges on the same face is R e q = 5 R 9 ii. If A B is removed, assuming the equivalent resistance between remaining resistors is x , 1 R e q = 1 R + 1 x R e q = R x R + x ∴    5 9 = 1 ( x ) 1 + x = x 1 + x                                         . . . . ∵   R = 1 Ω ∴    5 ( 1 + x ) = 9