In the arrangement of resistances as shown, what is the equivalent resistance between A and B? 

detailed solution

Correct option is D

We can simplify the circuit diagramAnd we can see that between A and C terminal 2r and 2r resistances are parallel combination and we can calculate by using the formulaReq=R1×R2R1+R2 Hence 2r×2r2r+2r=rSimilarly we can find the parallel combination between B and C terminal 2r×2r2r+2r=rAgain we can see that between C and D terminal r and r resistances are parallel combination and again we calculate by using formula Req=R1×R2R1+R2 hence we get r×rr+r=r2And now we get a simplifying circuitHence we can understand that it follows the wheatstone bridge concept and balance the following equation which is PQ=RSwhere P = Q = R = S = r Ω hence no current will be drawn from r2Ω resistance i.e.Equivalent resistance is 2r×2r2r+2r=r(Because r and r are in series combination so r + r = 2r)