A resistance of R draws current from a ...

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

\frac{1}{R_1} = \frac{1}{R} + \frac{1}{\frac{R_0}{2}}

Effective resistance between points A & B

R_2 = \left( \frac{R \cdot \frac{R_0}{2}}{R + \frac{R_0}{2}} \right) + \frac{R_0}{2}

Current drawn from the voltage source,

I = \frac{V}{R_2}

I = \frac{V}{\left( \frac{R \cdot \frac{R_0}{2}}{R + \frac{R_0}{2}} \right) + \frac{R_0}{2}}

Let current through

R

I_1

I_1 = \frac{I \left( \frac{R_0}{2} \right)}{R + \frac{R_0}{2}}

\text{Voltage across} R, V_1 = I_1 R

= \frac{I R_0}{2 \left( R + \frac{R_0}{2} \right)} \cdot R

= \frac{R R_0}{2 \left( R + \frac{R_0}{2} \right)} \cdot \frac{V}{\left( \frac{R R_0}{2R + R_0} \right) + \frac{R_0}{2}}

= \frac{2 R V}{R_0 + 4 R}

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