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# State the Principle of a Potentiometer. Define Potential Gradient. Obtain an Expression for Potential Gradient in Terms of Resistivity of the Potentiometer Wire. - Physics

ConceptPotentiometer

#### Question

State the principle of a potentiometer. Define potential gradient. Obtain an expression for potential gradient in terms of resistivity of the potentiometer wire.

#### Solution

Principle
When a constant current is passed through a wire of uniform area of cross-section, the potential drop across any portion of the wire is directly proportional to the length of that portion.
Let V be the potential difference across certain portion of the wire, whose resistance is R. If I is the current through the wire, then $V = IR$ We know that $R = \rho\frac{l}{A}$, where l, A and ρ are length, area of cross-section and resistivity of the material of the wire, respectively.

$\therefore V = I\rho\frac{l}{A}$

$\Rightarrow \frac{V}{l} = \frac{I\rho}{A}$

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Solution State the Principle of a Potentiometer. Define Potential Gradient. Obtain an Expression for Potential Gradient in Terms of Resistivity of the Potentiometer Wire. Concept: Potentiometer.
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