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 $\frac{5}{9} Ω$ . Now, if the resistor between $A$ and $B$ is removed, then find the new effective resistance (in $Ω$ ) between the same two points.

Question

TestHub · Accepted Answer

i. For a cube of resistors each of resistance $R$ the equivalent resistance between two edges on the same face is $R_{e q} = \frac{5 R}{9}$

ii. If $A B$ is removed, assuming the equivalent resistance between remaining resistors is $x,$

$\frac{1}{R_{e q}} = \frac{1}{R} + \frac{1}{x}$

$R_{e q} = \frac{R x}{R + x}$

$∴ \frac{5}{9} = \frac{1 (x)}{1 + x} = \frac{x}{1 + x} . . . . (∵ R = 1 Ω)$

$∴ 5 (1 + x) = 9 x$

$∴ 5 + 5 x = 9 x$

$∴ 5 = 4 x$

$∴ x = \frac{5}{4} Ω$

$∴ x = 1.25 Ω$

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