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. - Physics


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.



From the figure given in the question, current I through Ro is 


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 


Now R' and R are in parallel; therefore, voltage across R and R' is equal. Therefore, voltage across R is



Concept: Metre Bridge
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2013-2014 (March) All India Set 2

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