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Question

A resistance of R Ω draws current from a potentiometer. The potentiometer wire, AB, has a total resistance of R0 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 wire.
828479_36ed9c8d4b1b4a0ea284270d03eac580.jpg

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Solution

Let the length of coir AB be 'l'
mid point of AB be M
Voltage across AB is V
Potential gradient of AB=Vl
Since, sliding contact is at M
Voltage across resistance R will be equal to potential across AM
Voltage across R=(potential gradient of AB)×( length of AM)
=Vl×l2
=V2
Voltage acrossR=V2.

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