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Question

A battery of V voltage is connected across the potentiometer wire AC of total resistance R0 as shown. Calculate the potential across the resistance R if the sliding contact point B is exactly at the middle of the potentiometer wire.

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A
2VR4R0+R
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B
4VR02R0+R
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C
2VRR0+4R
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D
4VR0R0+2R
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Solution

The correct option is A 2VR4R0+R
When the slide is in the middle of the potentiometer only half of its total resistance
Therefore, R02 (Rlength) will be between A and B say R1 will be given by

1R0=1R+1R0

R1=R0RR0+2R
Total resistance between A and C will be the sum of the resistance between A & B and B & C, given by

R1+R02

The current flowing throughout the potentiometer is
I=VR1+R02=2V2R1+R0

The voltage V1 taken from potentiometer is given by
V1=IR1=2V2(R0RR0+2R)+R0×(R0RR0+2R)

V1=2VR2R+R0+2R=2VRR0+4R

Hence, Option A is the correct answer. which is 2VR4R0+R

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