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In the circuit shown, the resistance of ...

In the circuit shown, the resistance of each of resistor is `R=100Omega`. Find the nearest integer, which is to be connected points C and D so that the resistance of entire ciruit between A and B does not depend on the number of elementary cells.

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The correct Answer is:
`73`
Let resistance added across CD is x, then the equivalent resistance between A and B will be independent of the number of elementary cells if the combination of x with the resistors of the elementary cells is x it self. So `R_(AB)=x`
`:.x=((2R+x)xxR)/((3R+x))`
`impliesx=(sqrt(3)-1)xxR`
`=(1.73-1)xx100`
`=73Omega`
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