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.

Answer

A, B, C, D

Explanation

a., b.,c., d.
Potential difference across the terminals of the cell is given by
`V = E - ir`. Hence, the graph between V and i will be a straight
line having negative slope and positive intercept. Hence, (a) is
correct.
Total electrical power generated is Ei and thermal power
generated in the cell is `i^2r`. Hence, thermal power generated in
the external circuit is `P= Ei + i^2r`. So, the graph between P and
i is a parabola passing through the origin. Hence, choice (b) is
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 = V_i = V((E-V)/r) = (EV)/r - (V^2)/r`
Hence, the graph between P and V will be parabola passing
through the origin and have a maximum value of P at `V = E//R`.
Hence, choice (d) is correct.
At an instant, thermal power generated in the cell is equal to `i^2r` and total electrical power generated in the cell is equal to
Ei. Hence the fraction ` eta = i^2r//Ei = (r//E)i.`
Hence, the graph between `eta` and i will be a straight line passing
through the origin and have a positive slope. Hence, (c) is
correct.