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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. - CBSE (Science) Class 12 - Physics

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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`

∝ 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`

  Is there an error in this question or solution?
Solution 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. Concept: Metre Bridge.
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