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 $\mathrm{A}$ at $t=1 \mathrm{sec}$, then the balancing point will be obtained at (A) $t=3 \mathrm{~s}$ (B) $t=5 \mathrm{~s}$ (C) $t=4 \mathrm{~s}$ (D) $t=9 \mathrm{~s}$

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 $\mathrm{A}$ at $t=1 \mathrm{sec}$, then the balancing point will be obtained at
(A) $t=3 \mathrm{~s}$
(B) $t=5 \mathrm{~s}$
(C) $t=4 \mathrm{~s}$
(D) $t=9 \mathrm{~s}$

Key Concepts

Potential Gradient

The concept of a potential gradient refers to the constant voltage drop per unit length along a resistive wire when the current is uniform. In the potentiometer method, the uniformity of the potential gradient allows one to correlate the distance along the wire directly with the potential difference, making it possible to determine the value of an unknown EMF by simply measuring a length.

Potentiometer Principle

A potentiometer is an instrument used to measure the electromotive force (EMF) of a cell without drawing current from it. It does this by comparing the unknown voltage to a known potential difference created along a wire with uniform resistance distribution. The method relies on balancing the potential drop along the wire with the unknown EMF, thereby achieving a null measurement condition on a sensitive detector like a galvanometer.

Balancing Condition

At the balancing point in a potentiometer circuit, the voltage drop across a certain segment of the wire exactly equals the unknown EMF. This condition is identified by a zero reading on the galvanometer, indicating that no extra current flows into it. This makes the measurement accurate and immune to errors caused by the internal resistance of the cell or the measuring circuit.

Time-Dependent Circuit Analysis

In situations where circuit parameters, such as resistance, change with time, analyzing how these variations affect the circuit's behavior is crucial. Time-dependent analysis involves understanding transient responses, which can alter the current distribution and potential differences in the circuit, ultimately affecting the conditions required for achieving a balance in a potentiometric measurement.

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