Question

An electron in potentiometer wire experiences a force $2.4 \times {10^{ - 19}}N$. The length of the potentiometer wire is $6m$. The emf of the battery connected across the wire is (electronic charge =$1.6 \times {10^{ - 19}}C$).
A. $6V$
B. $9V$
C. $12V$
D. $15V$

Answer 1

In the question, we have a potentiometer wire of given length and force. We have to find the emf of the battery across the wire. We will use the formula for emf which is equal to the ratio of energy to the charge.

Complete step by step answer:
Consider a potentiometer wire of length $\left( l \right)$ of magnitude $6m$ experiences a force $\left( F \right)$ $= 2.4 \times {10^{ - 19}}N$. We had to find the electromotive force across the battery. Electromotive force is defined to be energy per unit electric charge imparted by the battery. As given in the question, the charge $\left( q \right)$ $= 1.6 \times {10^{ - 19}}C$

So, we need to find the energy first. Energy is the capacity of doing work.Using the formula of force, finding the energy $F = \dfrac{E}{d}$ where $E$ is the energy, $d$ is the distance but according to our question taking $l$
E = 2.4 \times {10^{ - 19}} \times 6 \\\ \Rightarrow E = 14.4 \times {10^{ - 19}} \\\
finally, $emf = \dfrac{E}{q}$
$emf = \dfrac{{14.4 \times {{10}^{ - 19}}}}{{1.6 \times {{10}^{ - 19}}}}$
$\therefore emf = 9V$

So, the correct option is B.

Note: Potentiometer is a three-terminal resistor that uses a sliding or rotating contact to form an adjustable voltage divider. It is used to control the voltage. Potential gradient of the potentiometer depends on the total voltage across the wire and the length of the wire. And it is independent of the density of the wire provided.