What is the resistance of $0.01 \mathrm{M} \mathrm{KCl}$ solution if its conductivity is $200…

What is the resistance of $0.01 \mathrm{M} \mathrm{KCl}$ solution if its conductivity is $200 \mathrm{ohm}^{-1} \mathrm{~cm}^{-1}$ and cell constant is $1 \mathrm{~cm}^{-1}$ ?
  1. $1 \times 10^{-3} \mathrm{ohm}$
  2. $5 \times 10^{-3} \mathrm{ohm}$
  3. $4 \times 10^{-3} \mathrm{ohm}$
  4. $2 \times 10^{-3} \mathrm{ohm}$

Solution

$\begin{aligned} & \text { Conductivity }=\frac{1}{\mathrm{R}} \cdot \frac{\ell}{\mathrm{A}} \\ & \frac{\ell}{\mathrm{A}}=\text { cell constant } \\ & 200=\frac{1}{\mathrm{R}} \times 1 \\ & \mathrm{R}=\frac{1}{200} \mathrm{ohm} \\ & \mathrm{R}=5 \times 10^{-3} \mathrm{ohm}\end{aligned}$

Asked in: MHT CET 2021 (22 Sep Shift 1)

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