Question

The SI unit of inductance, the Henry can be written as:
(This question has multiple correct options.)
A. $\dfrac{\text{Weber}}{\text{Ampere}}$
B. $\dfrac{\text{Volt-second}}{\text{Ampere}}$
C. $\dfrac{\text{Joule}}{{\left( \text{Ampere}\right)}^{2}}$
D. $\text{Ohm-second}$

Answer 1

Hint: In order to answer this question, you could recall certain expressions for inductance in terms of various physical quantities. You may recall the expression emf, then the expression for magnetic flux, and also the expression for energy stored in an inductor. Then, you could express them in terms of their respective units. Thus, you will find which among the given options correctly defines Henry.
Formula used:
Emf,
$\varepsilon =-L\dfrac{dI}{dt}$
Magnetic flux,
$\phi =LI$
Energy stored in an inductor,
$E=\dfrac{1}{2}L{{I}^{2}}$

Complete step-by-step solution
In the question, we are said that Henry is the SI unit of inductance and we are asked to find which among the given options are equivalent to Henry.
In order to answer this question, let us recall the expressions for inductance.
We know that emf is given by the relation,
$\varepsilon =-L\dfrac{dI}{dt}$
Let us express the terms in this relation in terms of their respective units, then,
$V=\left( H \right)\dfrac{A}{s}$
$\Rightarrow H=\dfrac{Vs}{A}$ ……………………………………… (1)
Therefore, we found that Henry could be given by $\dfrac{\text{Volt-second}}{\text{Ampere}}$.
Hence, option B is correct.
But, we know that,
$\dfrac{V}{A}=\Omega $
Substituting this in (1), we get,
$H=\Omega s$
Therefore, we found that Henry can also be expressed as $\text{Ohm-second}$. Hence, option D is also correct.
Now we could recall the expression for magnetic flux in terms of inductance which is given by,
$\phi =LI$
$\Rightarrow L=\dfrac{\phi }{I}$
When expressed in terms of the respective units of the quantities,
$H=\dfrac{Wb}{A}$
Therefore, we found that Henry can be expressed as $\dfrac{\text{Weber}}{\text{Ampere}}$. Hence, option A is also correct.
Now let us recall the expression for the energy of an inductor given by,
$E=\dfrac{1}{2}L{{I}^{2}}$
$\Rightarrow L=\dfrac{2E}{{{I}^{2}}}$
When expressed in terms of the respective units of the quantities,
$H=\dfrac{J}{{{A}^{2}}}$
Therefore, we found that Henry can be also expressed as $\dfrac{\text{Joule}}{{\left( \text{Ampere}\right)}^{2}}$ . Hence, we found that option D is also correct.
Therefore, all the given options are found to be correct.

Note: As it is mentioned that there is a possibility of multiple options being correct, you should expect a chance for all the options being correct. Inductance could be defined as the tendency of the conductor to oppose the change in current flow through it. A magnetic field is created as the result of this current flow.