In the figure, the value of resistors to be connected between C and D so that the resistance of the entire circuit between A and B does not change with the number of elementary sets used is

(1) R

(2) R(31)

(3) 3 R

(4) R(3+1)

(2) Cut the series from XY and let the resistance towards right of XY be R0 whose value should be such that when connected across AB does not change the entire resistance. The combination is reduced to as shown below.

The resistance across EF=REF=(R0+2R)

Thus RAB=(R0+2R)RR0+2R+R=R0R+2R2R0+3R=R0

R02+2RR02R2=0R0=R(31)

Difficulty Level:

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