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A potentiometer consists of a wire of length $4\,m$ and resistance $10\Omega $ . It is connected to a cell of e.m.f. $3V$ . The potential gradient of wire is.
A) $0.75\,V{m^{ - 1}}$
B) $2\,V{m^{ - 1}}$
C) $6\,V{m^{ - 1}}$
D) $10\,V{m^{ - 1}}$

Last updated date: 20th Jun 2024
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Hint:A potentiometer is an instrument used for measuring an electromotive force by balancing it against the potential difference produced by passing a known current through a known variable resistance. Find the current using ohm’s law. Potential gradient is the ratio of potential across potentiometer to the length of the potentiometer.

Complete step-by-step solution:
Potentiometer wire length, $l = 4\,m$
Resistance of the potentiometer, $R = 10\Omega $
Emf of the cell, $E = 3\,V$
We know that the potential gradient is the ratio of the potential difference across the potentiometer to the length of the potentiometer. The potential difference across the circuit is the same as the emf of the cell.
The potential gradient $k$ will be given as:
$k = \dfrac{V}{L}$
Here, $V$ is the potential difference which is the same as the emf of the cell. Substituting the values, we get
$k = \dfrac{{3V}}{{4m}}$
$ \Rightarrow k = 0.75\,V{m^{ - 1}}$
Therefore, the potential gradient of wire is $0.75\,V{m^{ - 1}}$ .
Thus, option A is the correct option.

Additional details: A potentiometer is a three-terminal resistor which has a sliding or rotating contact that forms an adjustable voltage divider. When only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat. A potentiometer is a measuring instrument which is essentially a voltage divider used for measuring electric potential (voltage); the component is an implementation of the same principle, hence its name. It is commonly used to control electrical devices such as volume controls for audio equipment.

Note:There is no use of the resistance given in the problem to find the value. Though without the resistance the circuit will not act as a potentiometer. The unit of potential gradient is $V{m^{ - 1}}$ . Potentiometer can also be considered as an absolute position sensing device.