(a, b, d)

Potential difference across the terminals of a cell is given by: V = E – ir. Hence, the graph between V and I will be a straight line having negative slope and a positive intercept on V-axis. Hence, the option is correct.

Total electric power generated in the cell is equal to Ei and thermal power generated in the cell is equal to i 2 r. Hence, the thermal power generated in the external circuit is P = Ei – i 2 r. Hence, the graph between P and I will be a parabola passing through origin, the slope of the parabola will be equal to = E – 2ir.

Hence, the slope of the curve will be maximum at r = 0 and then it decreases gradually but remains positive. Hence, the option is also correct. When terminal potential difference across the cell is V, current flowing through the circuit will be i = (E – V)/r and thermal power generated in the external circuit will be equal to

P = Vi = V(E – V)/r

Hence, the graph between P and V will be a parabola passing through origin and having maximum value of P at V = E/2. Hence, the option is also correct.

At an instant, thermal power generated in the cell is equal to i 2 r and total electrical power generated in the cell is equal to Ei. Hence, the fraction η = or, η = i or, η ∝ i.

Hence, the graph between η and i will be a straight line passing through origin and having a positive slope as shown in figure. Hence, the option is wrong.