Question

The SI unit of inductance, the henry can be written as
(a). weber/ ampere
(b). volt second/ ampere
(c). joule/ ${\text{ampere}}^2$
(d). all of the above

Answer 1

- Hint: Inductance is a property shown by an electrical conductor, in which the electric conductor induces an E.M.F in itself in order to oppose the change in the electric current flowing through it.

Complete step-by-step solution -

We know that, according to Faraday’s laws of induction, if there is a change in magnetic flux associated with a coil, there will be an e.m.f induced in the coil that opposes the change in magnetic flux associated with the coil.
In the case of an electric conductor, an e.m.f induced when there is a change in electric current which is flowing through the conductor. If L is the inductance of the conductor and I is the current flowing through it, the e.m.f ‘EMF’ induced can be written as,
$\text{EMF=}-L\left({\displaystyle \frac{dI}{dt}}\right)$ …… equation (1)
From equation (1) we know that the unit of ‘E’ is volt, current I is ampere and time is second. Writing the above equation in terms of units we get, (the negative sign is dropped since it does not affect the units)
$\text{volt=L}\left({\displaystyle \frac{\text{ampere}}{\text{second}}}\right)$
From this, we can get the unit of inductance L as,
$$\text{L=}\left({\displaystyle \frac{\text{volt}\text{.second}}{\text{ampere}}}\right)$$ ……… equation(2)
We are also familiar with the magnetic energy stored in an inductor of inductance L. The magnetic energy store in an inductor is given by,
$\text{E=}{\displaystyle \frac{\text{1}}{\text{2}}}\text{L}{\text{I}}^{\text{2}}$ ……….equation (3)
From equation(3) we know that the unit of energy is joules and current is ampere. So the unit of inductance can also be written as,
$\text{L=}{\displaystyle \frac{\text{joule}}{\text{amper}{\text{e}}^{\text{2}}}}$ ……… equation (4)

From Faraday’s induction laws it is clear that, the change in magnetic flux () associated with a coil produces an EMF in the coil given by,
$\text{EMF}=-\left({\displaystyle \frac{d\varphi }{dt}}\right)$ ………….equation (5)
Equation (1) and equation (5) are equal, so that we can equate,
$\left({\displaystyle \frac{d\varphi }{dt}}\right)=-L\left({\displaystyle \frac{dI}{dt}}\right)$
In terms of units we can write, weber is the unit of magnetic flux, ampere is the unit of current and second is the unit of time,
${\displaystyle \frac{\text{weber}}{\text{time}}}\text{=L}\left({\displaystyle \frac{\text{ampere}}{\text{time}}}\right)$
Therefore, the unit of L is,
$\text{L=}{\displaystyle \frac{\text{weber}}{\text{ampere}}}$ ……….equation (6)
Therefore, from equations (2), (4) and (6) we can say that the answer to the question is option (D)- all of the above.

Note: Inductance is a phenomenon present in almost all electrical circuits. If there is a change in current or voltage associated with an electric circuit, we can observe inductance. Inductors along with different capacitors and resistors are used to construct LCR circuits, which have various levels of application.