Question
Derive an expression for current flowing through a circuit when an external resistance is connected to a real $\text{e.m.f}$. device.
✓
Answer
$i$. If a current $(I)$ flows through an emf device, there is an internal resistance $(r)$ and the emf $(E)$ differs from the potential difference across its two terminals $(V).$
$V = E – Ir ……… (1)$
$ii$. The negative sign is due to the fact that the current $I$ flows through the emf device from the negative terminal to the positive terminal.
$iii.$ By the application of Ohm's law,
$V=I R ....... (2)$
From equations $(1)$ and $(2),$
$IR = E - Ir$
$\therefore \frac{E}{R+r}$
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