Question

What do you understand from the internal resistance of a cell? The potential difference of a cell becomes $1.8\,V$ when $0.5\,A$ current is drawn and when $1.0\,A$ current is drawn, it becomes $1.6\,V$ find the internal resistance of the cell and its emf.

Answer 1

Hint: In order to solve this question we need to understand what is current and how does it flow under potential difference. Current is defined as the charge crossing per unit area in unit interval of time. Actually, whenever a wire is subjected to potential difference then an electric field setup in wire forcing the free electrons to move in opposite direction of applied electric field which in turn causes current to flow in same direction as of electric field or the opposite direction of motion of electron.

Complete step by step answer:
Emf of a battery is defined as electromotive force which drives the electron inside battery in opposite direction and due to this force battery state changes and hence battery opposes this behavior and develops a resistance or opposition against it, since the resistance developed is inside battery so it is known as internal resistance of battery.

Consider a battery of emf $\varepsilon $ and internal resistance $r$. Let current $i$ be flowing inside the battery then from Kirchhoff’s law we get,
$V = \varepsilon - ir$
Whereas “$V$” is the potential difference across batteries.
So for case (i)
Given, $V = 1.8V$ when $i = 0.5A$
Putting values we get, $\varepsilon - 0.5r = 1.8 \to (1)$
And for case (ii)
Given, $V = 1.6V$ when $i = 1A$

Putting values we get,
$\varepsilon - r = 1.6 \to (2)$
So, simplifying both Equation by,
$E{q^n}(1) \times 2 - E{q^n}(2)$
We get,
$2\varepsilon - \varepsilon = 2(1.8) - 1.6$
$\Rightarrow \varepsilon = 2V$
Putting value of emf in equation number $1$ we get,
$2 - 0.5r = 1.8$
$\Rightarrow r = \dfrac{{0.2}}{{0.5}}\Omega $
$\therefore r = 0.4\Omega $

So internal resistance of the battery is $r = 0.4\Omega $ and the emf is $\varepsilon = 2V$.

Note: It should be remembered that current however has direction but it is not a vector instead it is a scalar quantity because current cannot be added by triangle law of vector addition so it cannot be regarded as vector. Also equation of continuity signifies that there should not be accumulation of charge at the junction so current entering the junction must leave the junction by the same amount.