Question

A battery of 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(s).

• A. internal resistance of battery is $5\Omega$
• B. emf of the battery is $20V$
• C. maximum current which can be taken from the battery is $4A$
• D. $V-i$ graph can never be straight line as shown in the 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 given figure(in problem).
The terminal voltage of the battery is given by
$V=E-Ir$.............................................................(1)
where, $r$ is the internal resistance of battery.
when $I=0,V=E$. Hence, $E=10$V.
Now, from graph, if $V=5$V, $I=1$A, therefore
$5=10-\left(1\right)r$...................................................from(1)
$r=5\Omega$
The maximum current which can be taken from the battery is
$I=\frac{E}{r}=\frac{10}{5}=2A$