Q. Battery shown in figure has $e$.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
Explanation
(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
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.