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.

Step-by-step solution

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