Question

Battery shown in figure has emf $E$ and internal resistance $r$. Current in the circuit can be varied by sliding the contact $J$.


If at any instant, current flowing through the circuit is $i$, potential difference between the terminals of the cell is $V$, thermal power generated in the external circuit is $P$ and the fraction of thermal power generated in the cell to the total electrical power generated in the circuit is equal to $\eta$, then which of the following graphs is/are correct ?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B)

Here, terminal voltage $V$ will be

$V=E–ir$

Hence, the graph between $V$ and $i$ will be a straight line having negative slope $r$ and positive intercept $E$. (option (a))

Thermal power generated in the external circuit

$P=Vi=Ei–i^{2}r$

Hence, the graph between $P$ and $i$ will be a parabola passing through the origin. (option (b))

Also at an instant, thermal power generated in the cell is $i^{2}r$ and total electrical power generated by the cell is $Ei$.

Hence, the fraction

$\eta =\frac{i^{2}r}{Ei}=\left(\frac{r}{E}\right)i$

So, $\eta \propto i$

It means the graph between $\eta$ and $i$ will be a straight line passing through the origin.

Hence, options $\left(a\right)$ and $\left(b\right)$ are the correct answers.