Question

Multiple correct answers type
The SI unit of inductance, Henry, can be written as:
$\begin{align}
  & A.\dfrac{weber}{ampere} \\
 & B.\dfrac{volt-second}{ampere} \\
 & C.\dfrac{joule}{amper{{e}^{2}}} \\
 & D.ohm- sec \\
\end{align}$

Answer 1

Hint: Use of formulas involving the inductance such as the voltage across the inductor, use the definition of Weber, and convert the units in terms of joules to get the units of the inductor in webers, joules, and other possible units. Express Weber in terms of volt-amperes to get the units in terms of volt-seconds if possible.

Step-by-step solution:

The voltage across the inductor is given by the expression :
$V = L \dfrac{di}{dt}$
We can write the inductance in terms of voltage current and time as :
$L = \dfrac{Vdt}{di}$
The units of the voltage are volt and units of time are seconds and the units of current are amperes
The units of the inductor can be found as by substituting the units of the voltage-current and time as units of L = $\dfrac{volt \times s}{A}$
Hence we found the units of the current in terms of volts seconds and the amperes as
$\dfrac{volt \times s}{A}$

The voltage across inductor can be written as according to the Faraday's law as the rate of change of flux linked with the inductor coils
We get voltage across inductor as $V = \dfrac{d\phi}{dt} = L \dfrac{di}{dt} $
Units of the flux are webers and the units of time are seconds :
Now substituting the units of flux and time we get the units of inductance as
$\dfrac{weber}{s} = L \times \dfrac{Ampere}{s} $
We get the units in terms of Weber as below :
Units of L are: $\dfrac{weber}{ampere}$
Hence we found the units of inductance in terms of webers as $\dfrac{weber}{ampere}$

Now we know the energy dissipated is given by E = Pt = VI t
Where is E is the energy dissipated, P is the power ad t is the time and power is written as VI
Now we know the units of energy as joules and we get the joules in terms of volt-amperes as
Joule = volt $\times$ ampere $\times$ sec
Volt-sec = $\dfrac{joule}{ampere}$
So substituting the volt second value in the first equation we get :
Units of L are : $\dfrac{joule}{ampere^2}$
Hence we found the units of inductance in terms of joules as $\dfrac{joule}{ampere^2}$
We also ohms are volt per ampere and hence the final option is also same as option B

Thus we have got all the options as the units of the inductance and hence the correct options are A, B, C, D.

Note: One of the main mistakes possible in this kind of problem is expressing the units in terms of webers. Here we need to apply Faraday's law which relates to the EMF of the inductor and the rate of change of flux linked with the coil of the inductor. We need to take care of this and in other cases the process will be time consuming and using the laws already available will help us solve all the problems quickly.