Battery shown in figure, has emf E and internal resistance r. Current in the circuit can be varied by sliding the contact J. If at an instant current flowing through the circuit is i, potential difference between terminals of the cell is V, thermal power generated in external circuit is P and thermal power generated in the cell is equal to η fraction of total electrical power generated in it, then which of the following graphs are correct ?

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Question

Battery shown in figure, has emf E and internal resistance r. Current in the circuit can be varied by sliding the contact J.

If at an instant current flowing through the circuit is i, potential difference between terminals of the cell is V, thermal power generated in external circuit is P and thermal power generated in the cell is equal to η fraction of total electrical power generated in it, then which of the following graphs are correct ?

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$i = \frac{ε}{r + R}$
V = ∈ – Ir
P = i²R       r + R = $\frac{ε}{i}$
$P = i^{2} [\frac{ε}{i} - r]$
$P = εI - i^{2} r$
$I^{2} r = εI - P$
$P = \frac{V^{2}}{R}$
$P = \frac{P}{i^{2}}$
$P = \frac{V^{2}}{P} \frac{(ε - V)^{2}}{r^{2}}$
$P = \frac{(ε - V) V}{r} = \frac{εV - V^{2}}{r}$