Question

The SI unit of inductance, the henry can be written as

• A. weber/ ampere
• B. volt second/ ampere
• C. joule/ $amper{e}^2$
• D. all of the above

Answer 1

The correct option is D all of the above

$e=\frac{d\varphi }{dt}=L\frac{dI}{dt}$

$\Rightarrow \left[volt\right]=\frac{\left[weber\right]}{\left[second\right]}=\left[L\right]\frac{\left[Ampere\right]}{\left[second\right]}$

also,

Energy dissipated(E) $=VIt$

$\Rightarrow \left[Joule\right]=\left[volt\right]\left[Ampere\right]\left[second\right]Rightarrow[volt-second]=\frac{\left[Joule\right]}{\left[Ampere\right]}$

so units of self inductance L is,

$\left[L\right]=\frac{weber}{Ampere}=\frac{volt-second}{Ampere}=\frac{Joule}{Amper{e}^2}$