# Emf of a Cell in an Open Circuit

Consider a cell having terminal voltage $V'$ and EMF, $V$ having internal resistance, $r$ and current, $I$ flows through the circuit in which an external resistance, $R$ is connected.

Potential drop across internal resistance= Ir

$$V= V' + Ir = IR + Ir$$

$$V=I(R+r)$$

Now if the cell is in an open circuit then $I=0$ and hence,
$V=0$

But we know that the Emf of the cell is equal to the Terminal Voltage of the cell in an open circuit, i.e.,
V=V'

Why such a contradiction in my concept?

I know how to derive $V=V'$. I don't need that. I want to know why using this concept makes Emf, $V= 0$ rather becoming $V=V'$.

• $V=I(R+r)$ applies to a closed circuit, where $I$ cannot be zero. – David White Sep 17 '19 at 15:39

$$V=EMF$$ $$V' = EMF- Ir$$