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Question

# The resistance a solution A is 50 ohm and that of solution B is 100 ohm, both solutions are taken in the same conductivity cell. If equal volumes of solution A and B are mixed, what is the resistance of the mixture using the same cell? (Assume there is no change or increase in the α of A and B on mixing)

A
R = 96.67 ohm.
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B
R = 76.67 ohm.
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C
R = 86.67 ohm.
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D
R = 66.67 ohm.
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Solution

## The correct option is D R = 66.67 ohm. How to approach this problem? First get conductivity for both the solutions in terms of cell constant. For solution A, Conductivity (kA) = G(Conductance) × G* (cell constant) =150G∗ For solution B, Conductivity(kB)=1100×G∗ ⋯(ii)(∵ G∗ is same for A and B) Now, When equal volumes of A and B are mixed, volume is the same and is DOUBLE of the initial volume in both the solutions. Hence, their individual contribution towards the conductivity of the mixture will be kA2 and kB2, respectively, and conductivity of the mixture will be (kA+kB2) or the mixture: (kA+kB2)=1R×G∗ ⋯(iii) From Eqs. (i), (ii) and (iii), we get R = 66.67 ohm.

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