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CBSE Class 12 Physics 2017 Delhi Set 1 Paper

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Question : 15
Total: 26
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.
Solution:  
Derivation of expression of voltage across resistance R

Resistance between points A & C
‌
1
R1
=‌
1
R
+‌
1
(‌
R0
2
)

Effective resistance between points A & B
R2=(‌
R
R0
2
R+‌
R0
2
)+‌
R0
2

Current drawn from the voltage source,
‌I=‌
V
R2

‌I=‌
V
(‌
R
R0
2
R+‌
R0
2
)+‌
R0
2

Let current through R be I1
I1=‌
I(
R0
2
)
R+‌
R0
2
‌‌ Voltage across ‌R,V1=I1R
‌=‌
IR0
2(R+‌
R0
2
)
⋅R
‌=‌
RR0
2(R+‌
R0
2
)
⋅‌
V
(‌
RR0
2R+R0
)+‌
R0
2
‌=‌
2RV
R0+4R
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