Question

When a conductance cell was filled with $0.0025M$ solution of an electrolyte, its resistance was $200ohm$. What will be the specific resistance (in $\Omega )$ of the electrolyte?

Given:
$\text{Length of cell}=100cm$
$\text{Cross-sectional area}=1.12\times {10}^{-4}c{m}^2$.

• A. $0.56\times {10}^{-4}$
• B. $1.12\times {10}^{-4}$
• C. $2.24\times {10}^{-4}$
• D. None of the above

Answer 1

The correct option is C $2.24\times {10}^{-4}$

From ohm's law
$V=I\times R$
$R=\frac{V}{I}$

$V:\text{Potential difference}R:\text{Electrical resistance}I:\text{Current}$​

The electrical resistance​ of a conductor is directly proportional ​to its length (l)​ and inversely proportional to its area of cross section (A).
$R\propto \frac{l}{A}$
$R=\rho \times \frac{l}{A}$
Where,
$\rho$ is constant of proportionality
This constant of proportionality is called resistivity or specific resistance.
$\text{Specific resistance,}\rho =R\times \frac{A}{l}$

$R=\frac{\text{Specific resistance}\times l}{A}$
$200=\frac{\text{Specific resistance}\times 100}{1.12\times {10}^{-4}}$
$\text{Specific resistance,}\rho =2.24\times {10}^{-4}$