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.
TEST PAPER 2006
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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
$1R_1 = 1R + 1R_02$
$R1 = RR_02R + R_0$
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
$I = VR_{1 }+ R_02= 2V2R_{1 }+ R_0$
The voltage $V_1$ taken from the potentiometer will be the product of current $I$ and the resistance $R_1$
$V_1 = IR_1 = 2V2R_1+ R_0 X R_1 = 2V_2RR_02R + R_0+ R_0 X RR_02R + R_0 = 2VRR_0 + 4R$
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