Question

the resistance of a solution "A" IS 50 OHMS AND THAT OF SOLUTION 'B' IS 100 OHMS BOTH SOLUTIONS BEING TAKEN IN THE SAME CONDUCTIVE CELL

IF EQUAL VOLUMES OF SOLUTION A AND B ARE MIXED WHAT WILL BE THE THE RESISTANCE OF THE MIXTURE USING THE SAME CELL.

Answer 1

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Answer 2

The resistance for the mixture is 66.67 ohms.

Given:

Resistance of solution A = 50 ohms

Resistance of solution B = 100 ohms

To find:

Resistance of the mixture = ?

Formula used:

Conductivity = Conductance $\bold{\times}$ Cell Constant

Conductance = 1/Resistance

Solution:

Let the conductivity of solution 'A' and 'B' is $\bold{K_1}$ and $\bold{K_2}$

Let the cell constant by 'x'

Conductivity of solution 'A' is:

$\bold{K_1=\frac{1}{50}\times x}$

Conductivity of solution 'B' is:

$\bold{K_2=\frac{1}{100}\times x}$

From question, the solutions are mixed i equal amount. Thus, the solution is diluted and the conductivity of the solutions is reduced by half.

Now, the conductivity of solution 'A' is:

$\bold{\Rightarrow \frac{K_1}{2}}$

Now, the conductivity of solution 'B' is:

$\bold{\Rightarrow \frac{K_2}{2}}$

Now, the conductivity of the mixture is:

$\bold{\Rightarrow \frac{1}{2}\times (K_1+K_2)}$

Now, the conductance and the resistance of the mixture is:

$\bold{\frac{1}{2}\times (K_1+K_2)=\frac{1}{R}\times x}$

On substituting the values of conductivity, we get,

$\bold{\frac{1}{2}\times ((\frac{1}{50}\times x)+(\frac{1}{100}\times x))=\frac{1}{R}\times x}$

$\bold{\frac{x}{100}+\frac{x}{200}=\frac{x}{R}}$

$\bold{x(\frac{2+1}{200})=\frac{x}{R}}$

$\bold{R=\frac{200}{3}}$

$\bold{R=66.67 \ \Omega}$