3 Marks Question

Question

Explain emf, potential difference and internal resistance of cell and derive the relation between them. (or derive the relation between emf, potential difference and internal resistance of the cell.)

Vidyadip · Accepted Answer

→The figure shows the electrolytic cell. Electrolytic cell is used to maintain a steady current in an electric circuit.
→As shown in the figure, two electrodes, positive (P) and negative (N) are immersed in an electrolytic solution.
→Because of being dipped in the solution, the electrodes exchange charges with the electrolyte.
→The potential difference between the positive electrode and the adjacent point A is $V _{+}$and the potential difference between negative electrode to the adjacent point B is $- V _{-}$.
→So, the potential difference between P and N is $V_{+}-\left(-V_{-}\right)=V_{+}+V_{-}$
→This potential difference is called the electromotive force (emf) of the cell and it is denoted by $\varepsilon$.
$\therefore \varepsilon= V _{+}+ V _{-}>0$
→Definition of emf : The potential difference between two electrodes when no current is flowing through the cell is called the emf of the cell.
→As shown in the figure, consider a resistor R connected across the cell and current I flows across R from C to D and current in electrolyte current flows from N to P . clearly, across the electrolyte →the same current flows through the electrolyte.
The electrolyte through which a current flows has a finite resistance $r \&$ it is called the internal resistance.
→Case I : $R =\infty$ (infinite)
According to ohm's law
$I =\frac{ V }{ R } \rightarrow I =0$
where V is the potential difference between P and N and it is called terminal voltage (or voltage) of the cell.
→The potential difference between P and N , V (terminal voltage or voltage)
$=$ Potential difference between P and A
+ Potential difference between A and B
+ Potential difference between B and N
$\begin{aligned}
V & = V _{+}+ V _{-} \\
\therefore V & =\varepsilon
\end{aligned}$
→Thus, emf $\varepsilon$ is the potential difference between the positive and negative electrodes in an open circuit i.e when no current is flowing through the cell.
→Case II : $R =$ Finite
when $R$ is finite, electric current flows through the cell. In that case the potential difference between P and N is
$\begin{aligned}
V & = V _{+}+ V _{-}- I r \\
\therefore \quad V & =\varepsilon- I r
\end{aligned}$
→The negative sign in the expression (Ir) for the potential difference between A and B . This is because the current I flows from B to A in the electrolyte.

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