A resistance of R draws current from a potentiometer. The potentiometer wire $, AB, $ has a total resistance of $R_o. A$ voltage $V$ is supplied to the potentiometer. Derive an expression for the voltage across $R$ when the sliding contact is in the middle of potentiometer wire.
CBSE DELHI - SET 2 2017
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When the slide is in the middle of the potentiometer, only half of its total resistance.
i.e. $R_02 \ ($since resistance is directly proportional to length$)$ will be between $A$ and point of contact $(C),$ say $R_1,$ will be given by the following expression $\ce{1R_1 = 1R + 1R_02 R1 = RR_02R + R_0}$
The total resistance between $A$ and $B$ will be sum of the resistance between $A C$ and $C B$ ie $R_1 + R_02$ Current flowing through the potentiometer will be $\ce{I = VR_{1 }+ R_02= 2V2R_{1 }+ R_0}$
The voltage $V_1$ taken from the potentiometer will be the product of current $I$ and the resistance $\ce{R_1V_1 = IR_1 = 2V2R_1+ R_0 X R_1 = 2V_2RR_02R + R_{0 }+ R_0 X RR_02R + R_0 = 2VRR_0 + 4R}$
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