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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 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.

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Solution

As the slide is in middle of the potentiometer only half of its resistance (R0/2) will be in parallel with the resistance R. Hence, the total resistance (R1) will be given by the following expression:

1R1=1R+1(R0/2)

R1=R0RR0+2R

The total resistance between A and C is R1+R0/2.

The current flowing through the potentiometer will be

I=VR1+R0/2=2V2R1+R0

The voltage V1 taken from the potentiometer will be the product of current I and resistance R1.

V1=IR1=(2V2R1+R0)×R1

Substituting for R1, we have

V1=2V2(R0×RR0+2R)+R0×R0R(R0+2R)

V1=2VR2R+R0+2R

V1=2VRR0+4R

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