Question

Battery shown in figurc has c.m.f. $E$ 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 terminals of the cell is $V$, thermal power generated in the cell is equal to $\eta$ fraction of total electrical power generated in it, then which of the following graphs is correct?

• A.
• B.
• C.
• D. Both (a) and (b) are correct

Answer 1

Answer: (D)

Terminal voltage $V=E-Ir$.
Hence, the graph between $V$ and $I$ will be a straight line having negative slope and positive intercept.
Thermal power generated in the external circuit,
$P=EI-I^{2}r.$
Hence, graph between $P$ and $I$ will be a parabola passing through origin.
Also at an instant, thermal power generated in the cell $=I^{2}r$ and total electrical power generated in the cell $=EI$.
Hence the fraction $\eta =\frac{I^{2}r}{EI}=\left(\frac{r}{E}\right)I;$
so $\eta \propto I$.
It means graph between $\eta$ and $I$ will be a straight line passing through origin.