Question

What is the value of $\text{1 Volt}$?
A. $\text{1 joule}$
B. $\text{1 joule per coulomb}$
C. $\text{1 coulomb per metre}$
D. $\text{1 Newton per coulomb}$

Answer 1

Hint: This problem can be solved by making use of the definition of one volt. One volt is the potential difference across a conductor when one joule of external work has to be done to bring a unit charge across it against the potential drop. Using this definition, and putting in the proper values, we can get a mathematical relationship for the value of one volt.

Formula used:
$1\text{ Volt = }\dfrac{1\text{ Joule}}{1\text{ Coulomb}}$

Complete step by step answer:
The potential difference across a conductor is a measure of the external work required to bring a unit charge across it against the potential gradient (that is, from lower potential to higher potential). Potential difference is measured in Volt $\left( V \right)$.
Therefore,
$\text{Potential difference = }\dfrac{\text{Work done to transfer the body across the potential gradient}}{\text{Charge of the body}}$
Now, the SI unit of work is Joule $\left( J \right)$ and the SI unit of charge is Coulomb $\left( C \right)$. Hence, by the definition of potential difference as given above, One volt is the potential difference across a conductor when one joule of external work has to be done to transfer a unit charge of one Coulomb across it from the lower to higher potential.
Hence, now putting the SI units in the ratio, we get
$1\text{ Volt = }\dfrac{1\text{ Joule}}{1\text{ Coulomb}}$
Hence, the value of 1 Volt will be $\text{1 joule per coulomb}$.
Therefore, the correct answer is B) $\text{1 joule per coulomb}$.

Note: Knowing the proper definitions of the physical quantities is imperative to solve such problems. In electromagnetism, electric potential and potential difference is one of the most basic quantities upon which the whole field of study is based. Often students don’t have proper knowledge of these basic quantities since they are used to define other important quantities. For example, capacitance is defined using charge and potential difference and students know its definition better than potential difference often. However, since the basic quantities form the whole subject, they should not be neglected. It is essential in physics that there is a deep understanding from the root level.