Question

The potentiometer wire $10 \mathrm{m}$ long and $20 \mathrm{ohm}$ resistance is connected to a 3 volts emf battery and a 10 ohms resistance. The value of potential gradient in volt / m of the wire will be
(A) 1.0
(B) 0.2
(C) 0.1
(D) 0.02

Answer 1

Hint To solve this question, we can use the concept that a potentiometer is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat. And also, it is used to compare the EMFs of different cells. It can also be used as a variable resistor in most of the applications. Potentiometers are commonly used to control electrical devices such as volume controls on audio equipment. Potentiometers operated by a mechanism can be used as position transducers, for example, in a joystick.

Complete step by step answer
Let us first define voltage drop. Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuit. Voltage drops in the internal resistance of the source, across conductors, across contacts, and across connectors are undesirable because some of the energy supplied is dissipated.
Total Voltage dropped in potential wire as: $=\mathrm{E}\left(\dfrac{\mathrm{R}}{\mathrm{R}+\mathrm{r}}\right)=3\left(\dfrac{20}{20+10}\right)=$
Now, we have to put values in the above expression to get: $3\left( \dfrac{20}{20+10} \right)V=2V$
Before moving forward let us define potential gradients. A potential gradient is the local rate of change of the potential with respect to displacement, i.e. spatial derivative, or gradient. This quantity frequently occurs in equations of physical processes because it leads to some form of flux.
We can add that voltage drop is not caused by poor connections, bad contacts, insulation problems, or damaged conductors; those are causes of voltage loss.
Now we can write that:
Potential Gradient $=\dfrac{\text { Potential Drop }}{\text { Length }}=\dfrac{2}{10}=0.2$ volt $/ \mathrm{m}$

Therefore, $\mathrm{B}$ is the correct option.

Note We need to know that the major disadvantage is that it requires a large force to move their sliding contacts that is wiper. There is wear and tear due to movement of the wiper. It reduces the life of this transducer. A potentiometer is a resistive-type transducer that converts either linear or angular displacement into an output voltage by moving a sliding contact along the surface of a resistive element. The potentiometer is also called a pot and is one of the most commonly used devices for measuring the displacement of the body. The potentiometer is the electrical type of transducer or sensor and it is of resistive type because it works on the principle of change of resistance of the wire with its length.