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 `)`.

Answer

`R=66.67ohms`

Explanation

`R_(A)=500Omega, R_(B)=100Omega`
`K_(A)=(1)/(50)xx(l)/(A) & K_(B)=(1)/(100)xx(l)/(A)`
When equal volumes one taken the
`K_("resultant")=(1)/(R^(1))x(2l)/(A)=(1)/(50)xx(l)/(A)+(1)/(100)xx(l)/(A)`
`(2)/(R^(1))=(150)/(50xx100)impliesR^(1)=(2xx50xx100)/(150)=(200)/(3)=66.7Omega`