  Question

Solution A,B and C of the same strong electrolyte offered resistances 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 Ω  B
81.8 Ω  C
100 Ω  D
300 Ω  Solution

The correct option is A $$67.3\ \Omega$$Let value be $$v_1,\ v_2$$ and $$v_3$$$$\dfrac {v_1}{R_1}+\dfrac {v_2}{R_2}+\dfrac {v_3}{R_3}=\dfrac {v_1 +v_2 +v_3}{Req}$$$$R_1=52\ \Omega\ R_2=100\ \Omega \ R_3=150\ \Omega$$$$v_1=\dfrac {1}{50}\ v_2=\dfrac {1}{100}\ v_3=\dfrac {1}{150}$$$$\dfrac {v_1}{R_1}+\dfrac {v_2}{R_2}+\dfrac {v_3}{R_3}=\dfrac {v_1 +v_2 +v_3}{Req}$$$$\dfrac {1}{50\times 50}+\dfrac {1}{100\times 100}+\dfrac {1}{150\times 150}=\dfrac {\dfrac {1}{50}+\dfrac {1}{100}+\dfrac {1}{150}}{Req}$$$$\dfrac {36+9+4}{150\times 50\times 4}=\dfrac {\dfrac {6+3+2}{900}}{Req}$$$$Req\ \dfrac {49}{150\times 150\times 4}=\dfrac {11}{300}$$$$Req\ =\dfrac {3300}{49}=67.3\ \Omega$$Chemistry

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