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Question
A resistance of R Ω draws current from a potentiometer as shown in the figure. The potentiometer has a total resistance Ro Ω. 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.
Solution
From the figure given in the question, current I through Ro is
`I=V/R_o`
Now, the sliding contact is in the middle of the wire. From the relation `R=rhol/A`
R ∝ l (where ρ and A are constants)
where l is the length of the wire, ρ is the resistivity and A is the area of the wire.
∴ Resistance of half of the wire of the potentiometer is
`R'=R_o/2`
Now R' and R are in parallel; therefore, voltage across R and R' is equal. Therefore, voltage across R is
`:.V'=I.R'=V/R_o"."R_o/2`
`=>V'=V/2`
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