Question

For electrolytes, Ohm's Law may be written as:
(A) $\dfrac{V}{I} = R$
(B) $\dfrac{{V + {V_{back}}}}{I} = R$
(C) $\dfrac{{V - {V_{back}}}}{I} = R$
(D) $\dfrac{{{V_{back}} - V}}{I} = R$

Answer 1

Hint To solve the question, you do not need any extra knowledge, just the usual meaning and concept of resistance is sufficient enough to reach at the answer to the question. Resistance is nothing but the ratio of potential difference across a section and the current flowing through that particular section.

Complete step by step answer:
As explained in the hint section of the solution to the question, the Ohm’s law for electrolytes is not much different from the usual Ohm’s law that we applied in the electricity and current section of the physics. The basic concept of resistance still remains the same, only the expression has changed a little bit since we cannot directly find the potential difference across electrolyte that easily as we could do with the case of solid metal wires.
Resistance is still the hindrance offered by the medium for the current to travel across it.
The Ohm’s law for electrolytes is defined as:
The resistance offered by the electrolyte is the ratio of the potential difference applied to the electrolyte and the current passing through the electrolyte.
This means that the resistance can be given as:
$R = \dfrac{{\Delta V}}{I}$
Where, $R$ is the resistance offered by the electrolyte
$\Delta V$ is the potential difference across the electrolyte
$I$ is the current flowing through the electrolyte
To define $\Delta V$ more clearly, we need to check the direction of the current that is flowing in the electrolyte, and for that, we can simply define the potential at the side from which the current is coming as ${V_{back}}$ and the potential at the other side as $V$. Using this, our relation becomes:
$R = \dfrac{{V - {V_{back}}}}{I}$
As we can see, this equation matches with the equation given in the option (C).

Hence, option (C) is the correct answer to the question.

Note The main issue where students have is the confusion between whether the option (C) is correct or the option (D) since both of the options include the magnitude $\Delta V$ as the numerator. To solve the confusion, you need to consider the direction of current and select the option accordingly, reaching at the option (C) as the correct answer.