A potentiometer is a device used for measuring EMF and...

A potentiometer is a device used for measuring EMF and internal resistance of a cell. It consists of two circuits, one is main circuit in which there is a cell of given emf $\varepsilon^{\prime}$ and given resistance $R$ which is connected across a wire of length $100 \mathrm{~cm}$ and having resistance $r$ and another circuit having unknown EMF $\varepsilon$ and galvanometer. For a given potentiometer, if $\varepsilon^{\prime}=30 \mathrm{~V}, r=1 \Omega$, and resistance $R$ varies with time $t$ given by $R=2 t$. The jockey can move on wire with constant velocity $10 \mathrm{~cm} / \mathrm{s}$ and switch $S$ is closed at $t=0$If jockey starts moving from $A$ at $t=0$ and balancing point found at $t=1 \mathrm{~s}$ then the value of $\varepsilon$ is (A) $1 \mathrm{~V}$ (B) $2 \mathrm{~V}$ (C) $3 \mathrm{C}$ (D) $4 \mathrm{~V}$

A potentiometer is a device used for measuring EMF and internal resistance of a cell. It consists of two circuits, one is main circuit in which there is a cell of given emf $\varepsilon^{\prime}$ and given resistance $R$ which is connected across a wire of length $100 \mathrm{~cm}$ and having resistance $r$ and another circuit having unknown EMF $\varepsilon$ and galvanometer. For a given potentiometer, if $\varepsilon^{\prime}=30 \mathrm{~V}, r=1 \Omega$, and resistance $R$ varies with time $t$ given by $R=2 t$. The jockey can move on wire with constant velocity $10 \mathrm{~cm} / \mathrm{s}$ and switch $S$ is closed at $t=0$If jockey starts moving from $A$ at $t=0$ and balancing point found at $t=1 \mathrm{~s}$ then the value of $\varepsilon$ is
(A) $1 \mathrm{~V}$
(B) $2 \mathrm{~V}$
(C) $3 \mathrm{C}$
(D) $4 \mathrm{~V}$

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Key Concepts

Potentiometer Principle

A potentiometer is an instrument used to measure electromotive force (EMF) by balancing a known voltage drop against an unknown EMF without drawing current from the source. It relies on a uniform potential gradient along a resistive element, which allows for accurate and current?independent measurements.

Potential Gradient

The potential gradient is the voltage drop per unit length along the potentiometer’s wire. This gradient is crucial because it establishes a linear relationship between distance along the wire and voltage, enabling the determination of the unknown EMF when the balancing point is found.

Balancing Condition

The balancing condition occurs when the voltage drop along a certain portion of the potentiometer wire exactly equals the unknown EMF. At this point, no current flows through the galvanometer, implying a null condition that allows for precise measurement of the EMF without interference from the cell's internal resistance.

Voltage Division

Voltage division in the context of a potentiometer refers to the distribution of the total applied voltage across a resistive wire in proportion to the lengths of wire segments. This principle allows the meter to compare the unknown EMF with the voltage drop across a selected portion of the wire, ensuring an accurate reading at the balancing point.

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