Question

A resistance of $R$ $\Omega$ draws current from a potentiometer. The potentiometer wire, $AB$, has a total resistance of $R_0$ $\Omega$. A voltage $V$ is supplied to the potentiometer. Derive an expression for the voltage across $R$ when the sliding contact is in the middle of the potentiometer wire.

Answer 1

Let the length of coir AB be 'l'

mid point of AB be M

Voltage across AB is V

$\Rightarrow$ Potential gradient of AB$=\frac{V}{l}$

Since, sliding contact is at M

$\Rightarrow$ Voltage across resistance R will be equal to potential across AM

$\Rightarrow$ Voltage across $R=($potential gradient of AB$)\times ($ length of AM$)$

$=\frac{V}{l}\times \frac{l}{2}$

$=\frac{V}{2}$

$\Rightarrow$ Voltage across$R=\frac{V}{2}$.