A resistance of R draws current from a potentiometer. The potentiometer wire, AB, has a total resistance of R0 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.
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The voltage across R when the sliding contact is in the middle of potentiometer wire is V1 = 2VR / Ro + 4R
Explanation:
When the slide is in the middle then its total resistance i.e Ro/2 between the points will be
1/R1 = 1/R + 1/Ro/2
R1 = 2 RRo / 2R + Ro
The total resistance between A Nd B will be the sum of resistance A and C.
That is R1 + Ro / 2
Current flowing through the potentio meter will be
I = V / R1 + ro / 2 = 2V / 2R1 + Ro
The voltage V1 from the potentiometer will be the product of current and the resistance R1.
V1 = IR1 = 2V / 2R1 + Ro x R1 = 2v / 2RRo / 2R +Ro + Ro = 2VR / Ro + 4R
Thus the voltage across R when the sliding contact is in the middle of potentiometer wire is V1 = 2VR / Ro + 4R
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