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 `)`.

Options

A. 66.66 `omega`
B. 63.65 `omega`
C. 52.36 `omega`
D. 59.38 `omega`

Explanation

Given resistance of A= 50 `omega` and resistance of B= 100 `omega` let us suppose `k_(1)` and `k_(2)` are the specific conductances of solution s A and B respecitvely and cell constant is y we know that
Specific conductance `=("cell constant")/("Resistance")`
For A `k_(1)=1/50 xx y`
For B `k_(2)=1/100 xx y` when equal volumes of A and B are mixed the volume becomes double then
specific conductance of mixture `=(K_(1)+k_(2))/(2)`
`therefore (k_(1)+k_(2))/(2)=(1)/(R )xx y`
`1/2(y)/(50)+(x)xx y`
`rarr 1/100+21/200=(1)/(R )`
`R=200//3=66.66 omega`