CBSE Class 12 Physics 2017 Delhi Set 1 Paper

Question : 15 of 26

Marks: +1, -0

A resistance of

R

draws current from a potentiometer. The potentiometer wire,

A B

, has a total resistance of

R_0

. 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}/{R_1}=\;{1}/{R}+\;{1}/{ (\;{R_0}/{2}) }

Effective resistance between points A & B

R_2= (\;{R {R_0}/{2}}/{R+\;{R_0}/{2}}) +\;{R_0}/{2}

Current drawn from the voltage source,

\;I=\;{V}/{R_2}

\;I=\;{V}/{ (\;{R {R_0}/{2}}/{R+\;{R_0}/{2}}) +\;{R_0}/{2}}

Let current through

R

I_1

I_1=\;{I ({R_0}/{2}) }/{R+\;{R_0}/{2}}

\;\;\text " Voltage across "\; R, V_1=I_1 R

\;=\;{I R_0}/{2 (R+\;{R_0}/{2}) } ⋅ R

\;=\;{R R_0}/{2 (R+\;{R_0}/{2}) } ⋅ \;{V}/{ (\;{R R_0}/{2 R+R_0}) +\;{R_0}/{2}}

\;=\;{2 R V}/{R_0+4 R}

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