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 cells 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 ?

Options

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

Answer

D

Explanation

(d) Terminal voltage `V = E - Ir`. Hence, the graph between `V` and `i` will be a straigh line having negative slopw and positive intercept
Thermal power generated in the exteranl 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 `=E i`. Hence the fraction `eta = (I^(2) r)/(EI) = ((r)/(E)) I`, so `eta prop I`. If means graph between `eta` and `I` will be a straight line