Question

The SI unit of inductance, the henry can be written as ……………
a. Weber/Ampere.
b. Volt second/Ampere.
c. Joule/Ampere square.
d. Ohm second.

Answer 1

Hint: The standard unit of inductance is directly proportional to induced flux an inversely proportional to flowing current through the flux. Based on this write the corresponding SI units and derive the unit of inductance.

Complete step by step answer:
The unit of inductance is henry (H) which is explained as the amount of inductance that causes a voltage of one volt, when the current is changing at a rate of one ampere per second. Henry is discovered by Joseph Henry.
The induced voltage from electromotive force can be expressed as –
$e=L\dfrac{dI}{dt}$
The above equation can be written using corresponding SI units, as
$\Rightarrow \left[ \text{volt} \right]=\left[ L \right]\left[ \dfrac{\text{Ampere}}{\text{second}} \right]$
This can be written as,
$\left[ L \right]=\left[ \dfrac{\text{Volt - second}}{\text{weber}} \right]$
So, the SI unit of inductance is Volt second/Ampere.
Similarly, the inductance is also the ratio of magnetic flux to current, i.e.,
$L=\dfrac{\phi }{I}$
We know the SI unit of flux is weber, so the SI unit of inductance based on the above equation is weber/Ampere.
Now the energy stored by magnetic field of inductor is given by the formula,
$W=\dfrac{1}{2}L{{I}^{2}}$
Here W is the energy store, its SI unit is Joules. L is the inductance and I is the current.

$E=VIt$
Writing the corresponding SI units, we get
$\Rightarrow \left[ \text{Joule} \right]\text{=}\left[ \text{volt} \right]\left[ \text{Ampere} \right]\left[ \text{second} \right]$
Equating equation (i) and (ii), we get
$\begin{align}
  & \left[ L \right]=\dfrac{\text{weber}}{\text{Ampere}}\text{=}\dfrac{\text{volt-second}}{\text{Ampere}} \\
 & \left[ L \right]=\dfrac{\text{Joule}}{\text{Amper}{{\text{e}}^{\text{2}}}} \\
\end{align}$
So, the unit of self-inductance ‘L’ is Joule/Ampere square.
Hence, all the options are correct.

Additional Information:
Inductance is the impulse of an electrical conductor to deny a shift in the electric current flowing through it. The inductance was invented by Oliver Heaviside in 1886. It is explained as the ratio of the induced voltage to the assess of change of current creating it. It is based on the geometry of the circuit conductor and magnetic permeability of adjacent materials.
“Any change in magnetic field through a circuit induces an electromagnetic force (EMF) in the form of voltage in the conductors”, stated Faraday’s law of inductance. It is also termed as electromagnetic induction. Hence the varying current induces a voltage in the conductor.
This induces voltage in a direction which tends to oppose the change in current by Lenz's law, the back emf has produced. A conductor’s inductance opposes any variation in electric current through it due to back EMF.

Note: Always remember that the ratio of magnetic flux to flowing current is called inductance.
Students often stop solving the question once they get an option as correct. They should always check for other options too.