The resistance of a solution `A` is `50 ohm` and that of solution `B` is `100ohm,` 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 `prop` of `A` and `B` on mixing `)`.

Explanation

For solution `A`,
Conductivity `(k_(A))=G(` Conductance `)xxG^(**)(` cell conostant `)`
`=(1)/(50)xxG^(**)" "(i)`
For solution `B`,
Conductivity `(k_(B))=(1)/(100)xxG^(**)" "(ii)( :' G^(**) is same fo r A and B)`
When equal volumes of `A` and `B` are mixed, dilution becomes doubled in both teh solutions. Hence, thir individual contribution towards the conductivity of the mixture will be `k_(A)//2` and `k_(B)//2` , respectively, and conductivity of the mixture will be `((k_(A)+k_(B))/(2))`
For the mixture `:((k_(A)+k_(B))/(2))=(1)/(R)xxG^(**)" "(iii)`
From `Eqs. (i), (ii) ` and `(iii),` we get
`R=66.67 ohm`