Question

A potentiometer is connected between A and B and the balance point is obtained at $203.6cm$. When the end of the potentiometer connected to B is shifted to C, then the balance point is obtained at $24.6cm$. If now the potentiometer be connected between B and C, the balance point will be at:

• A. $179.0cm$
• B. $197.2cm$
• C. $212.0cm$
• D. $228.0cm$

Answer 1

The correct option is A $179.0cm$

Let the potential gradient of the potentiometer be $x$.

$x=\frac{E}{L}$

or $x=\frac{v}{L}$

When potentiometer connected between $AB$

$v={ϵ}_1$ and $l=20.6cm$

$\therefore x=\frac{{ϵ}_1}{203.6}$

$⟹{ϵ}_1=203.6x\to \left(1\right)$

When it is connected between $AC$ then

$v={ϵ}_1-{ϵ}_2$ and $l=24.6x\to \left(2\right)$

Subtracting equation $\left(1\right)$ and $\left(2\right)$

${ϵ}_1=203.6x$

$v={ϵ}_1-{ϵ}_2=24.6x$

${ϵ}_2=(203.6-24.6)x$

${ϵ}_2=179x$

$⟹x=\frac{{ϵ}_2}{179}$

There when potentiometer is connected between $B$ and $C$ then the balance point will be $179cm$