potentiometer

Question

A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. ${E}_{0}$ and a resistance ${r}_{1}$. An unknown e.m.f. E is balanced at a length $\mathcal{l}$ of the potentiometer wire. The e.m.f. E will be given by

Moderate

Solution

The current through the potentiometer wire is

$I=\frac{{E}_{0}}{\left(r+{r}_{1}\right)}$

and the potential difference across the wire is

$V=Ir=\frac{{E}_{0}r}{\left(r+{r}_{1}\right)}$

The potential gradient along the potentiometer wire is

$k=\frac{V}{L}=\frac{{E}_{0}r}{\left(r+{r}_{1}\right)L}$

As the unknown e.m.f. E is balanced against length $\mathcal{l}$ of the potentiometer wire,

$\therefore E=kl=\frac{{E}_{0}r}{\left(r+{r}_{1}\right)}\frac{l}{L}$

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