The resistance of a conductivity cell filled with $0.1 \ M$ $KCl$ solution is $100 \ \Omega$. If the resistance of the same cell when filled with $0.02 \ M$ $KCl$ solution is $520 \ \Omega$,the molar conductivity of $0.02 \ M$ solution (in $S \ cm^2 \ mol^{-1}$) is (Given: conductivity of $0.1 \ M$ $KCl$ solution $= 1.29 \ S \ m^{-1}$)

An electrolyte of a polymer-salt complex of poly(ethylene oxide)-LiCF$_{3}$SO$_{3}$ is shaped into a free standing circular film of $20 \ mm$ diameter and a thickness of $20 \ \mu m$. When it is sandwiched between $2$ stainless steel circular electrodes of the same diameter, this cell exhibits a conductance of $\frac{314}{5} \ S$. What is the specific conductivity of the electrolyte?

If the distance between two $Pt$ electrodes is $2 \, cm$,the cross-sectional area is $4.0 \, cm^2$,and the resistance is $25 \, \Omega$,find the molar conductivity of a $0.5 \, M$ solution.

The conductivity of $0.02 \text{ M}$ $KCl$ solution at $298 \text{ K}$ is $0.0123 \text{ } \Omega^{-1} \text{ cm}^{-1}$. If the resistance of the cell containing this solution is $120 \text{ } \Omega$, what is the value of the cell constant (in $\text{ cm}^{-1}$)?

Conductivity of $0.001 \ M$ aqueous solution of $Na_2SO_4$ is found to be $2.6 \times 10^{-3} \ S \ cm^{-1}$ at $25 \ ^oC$. If limiting molar conductance of $Na^+$ is $50 \ S \ cm^2 \ mol^{-1}$,then limiting molar conductance of $SO_4^{2-}$ will be .............. $S \ cm^2 \ mol^{-1}$ (neglect conductivity of water).

Which of the following decreases on dilution of an electrolytic solution?