Question

Solution A, B and C of the same strong electrolyte offered resistance of $50\Omega$, $100\Omega$ and $150\Omega$ in a given conductivity cell. The resistance observed if they are mixed in a volume proportion which is reciprocal of their resistances and tested in the same conductivity cell would be:

• A. $67.3\Omega$
• B. $81.8\Omega$
• C. $100\Omega$
• D. $300\Omega$

Answer 1

The correct option is A $67.3\Omega$

Let volume be $V_1,V_2$ and $V_3$

$\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3}=\frac{V_1+V_2+V_3}{Req}$

$R_1=50\Omega R_2=100\Omega R_3=150\Omega$

$V_1=\frac{1}{50}{V}_2=\frac{1}{100}{V}_3=\frac{1}{150}$

$\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3}=\frac{V_1+V_2+V_3}{Req}$

$\frac{1}{50\times 50}+\frac{1}{100\times 100}+\frac{1}{150\times 150}=\frac{\frac{1}{50}+\frac{1}{100}+\frac{2}{150}}{Req}$

$\frac{36+9+4}{150\times 150\times 4}=\frac{\frac{6+3+2}{300}}{Req}$

$Req\frac{49}{150\times 150\times 4}=\frac{11}{300}$

$Req=\frac{3300}{49}=67.3\Omega$