A resistance or R ohm draws a current from a potentiometer.The potentiometer has a total resistance R0 ohm.A voltage V is supplied to the potentiometer .Derive an expression for the voltage fed to the ckt when the slide is in the middle of the potentiometer.

The following figure show the arrangement:





When the slide is in the middle of the potentiometer only half of its total resistance,i.e.,R02 Since R  length will be between A and B, say R1, will be given by the the following expression:1R1 = 1R + 1R02R1 = R0RR0+2RThe total resistance between A and C will be sum of the resistance between A & B and B&C,i.e.,R1 + R02The current flowing throught he potentiometer will be I = VR1 + R02 = 2V2R1  + R0 The voltage V1 taken from the potentiometer will be the product of current I and the resistance R1,V1 = IR1 = 2V2 R0RR0+2R+R0 × R0RR0+2RV1 = 2VR2R + R0 + 2R = 2VRR0 + 4R
 

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