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

Let us suppose k1 and k2 are the specific conductance of solutions ‘A’ and ‘B’ respectively and cell constant is ‘y’. We know that, Specific conductance=Conductance×Cell constant
For `(A).k_1=1/(50)xxy" For "(B), k_2=1/(100)xxy`
When equal volume of (A) and (B) are mixed, the volume becomes double. Then
Specific conductance of mixture `=(k_1+k_2)/(2)`
`:. (k_1+k_2)/(2)=1/Rxxy" "1/2[y/(50)+y/(100)]=1/Rxxy`
`1/(100)+1/(200)=1/R`
R=200/3=66.66 ohm