Question

A resistance of 50 $\Omega$ is registered when two electrodes are suspended into a beaker containing a dilute solution of a strong electrolyte such that exactly half of the them are submerged into solution. If the solution is diluted by adding pure water (negligible conductivity) so as to just completely submerge the electrodes, the new resistance offered by the solution would be:

• A. 50 $\Omega$
• B. 100 $\Omega$
• C. 25 $\Omega$
• D. 200 $\Omega$

Answer 1

The correct option is A 50 $\Omega$

The expression for the resistance of the solution is:

$R=\frac{1}{k}\frac{l}{A}$

Initially, only half of the electrodes were submerged but after dilution, they are completely submerged. Hence, the value of the area of electrode A in the above equation is doubled.

Due to the dilution, the volume of the solution is doubled and the molar concentration is reduced to half. Due to this, the value of specific conductance k is reduced to half.

Thus k is halved while the A is doubled. Hence R remains the same, i.e., 50 $\Omega$.