• # question_answer A resistance of $R\,\Omega$ draws current from a potentiometer. The potentiometer has a total resistance of ${{R}_{0}}\,\Omega .$ A voltage V is supplied to the potentiometer. Derive an expression for the voltage fed into the circuit when the slide is in the middle of the potentiometer.

The equivalent resistance of the circuit             ${{R}_{aq}}=\frac{{{R}_{0}}}{2}+\frac{R\cdot ({{R}_{0}}/2)}{R+({{R}_{0}}/2)}$ $\therefore$      Current in the circuit, $I=\frac{N}{{{R}_{aq}}}$ $V=I{{R}_{aq}}=I\left[ \frac{{{R}_{0}}}{2}+\frac{R\cdot ({{R}_{0}}/2)}{R+({{R}_{0}}/2)} \right]$             $=I\left( \frac{{{R}_{0}}}{2}+\frac{R{{R}_{0}}}{2R+{{R}_{0}}} \right)$ $\therefore$      $V=\frac{I{{R}_{0}}}{2}\left( 1+\frac{2R}{2R+{{R}_{0}}} \right)$