Question

A battery of $\text{EMF}$ $E$ and internal resistance $r$ is connected across a resistance $R$. Resistance $R$ can be adjusted to any value greater than or equal to zero. A graph is plotted between the current $\left(i\right)$ passing through the resistance and potential difference $\left(V\right)$ across it. Select the correct alternative.

• A. Internal resistance of battery is $5\Omega$.
• B. $\text{EMF}$ of the battery is $20\text{V}$.
• C. The maximum current which can be taken from the battery is $4\text{A}$.
• D. $V-i$ graph can never be a straight line, as shown in figure.

Answer 1

The correct option is A Internal resistance of battery is $5\Omega$.

Some devices having negative resistance show the inverse variation between voltage and current as shown in figure (in problem). So, option (d) is the wrong answer.

The terminal voltage of the battery is given by, $$V=E-Ir...\left(1\right)$$ where, $r$ is the internal resistance of battery.

When $I=0,V=E$. Hence, $E=10\text{V}$.

Now, from graph, if $V=0\text{V}$, $I=2\text{A}$,

So, $0=10-2\times r$

$\Rightarrow r=5\Omega$

The maximum current which can be taken from the battery is, $I=\frac{E}{r}=\frac{10}{5}=2\text{A}$

Hence, option (a) is the correct answer.