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At what value of the resistance in the c...

At what value of the resistance in the circuit shown in the figure will the total resistance between points A and B be independent of the number of cells? If `R = (sqrt(3)+1)Omega`, then the value of x will be `"…….."`Q.

Text Solution

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The correct Answer is:
B
`x = ((2R+x)R)/(3R+x)`
`3Rx + x^2 = 2R^2 + Rx `
`x^2 + 2Rx - 2R^2 = 0`
`x = -2R+-(sqrt(4R^2+8R^2))/2 = R(sqrt3 -1)`
`= (sqrt(3) + 1) (sqrt(3) -1) = 3-1 = 2Omega`.
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