Question

A resistance of R $\Omega$ draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance $R_0\Omega$. 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.

Answer 1

When the sliding contact is in middle, a resistance of $R_o/2$ is connected in series with a parallel combination of $R$ and $R_o/2$.

Hence, net resistance is given by:

$R_{eq}=\frac{R_o}{2}+\frac{R_o}{2}||R$

Current flowing through the circuit is given by:

$I=\frac{V}{R_{eq}}$

Potential across R is given by:

$V_R=I\left(\frac{R_o}{2}||R\right)$

$V_R=\frac{V}{R_{eq}}\left(\frac{R_o}{2}||R\right)$

Solving, $V_R=\frac{R}{4R+R_o}V$