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

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TestHub · Accepted Answer

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 itself. So R AB = x ∴ x = 2 R + x × R 3 R + x ⇒ x = 3 - 1 × R = 1.73 - 1 × 100 = 73 Ω

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