Question

Define 1 Henry in terms of unit.

Answer 1

Hint: One Henry is the value of self-inductance in a closed circuit or coil in which when we variate the inducing current by $1$ ampere per second and then one volt is produced. It is the S.I. unit of inductance.

Complete solution:
The inductance of an electric circuit is one Henry when an electric current is varying at one ampere per second gives an electromotive force of one volt across the inductor:
$V(t)=L{\displaystyle \frac{dI}{dt}}$
Where $V(t)$ is the resulting voltage across the circuit,
$I(t)$ is the current flowing through the circuit.
$L$ is the inductance of the circuit.
Henry is a derived unit based on four fundamental units, i.e., kilogram $(kg)$, meter $(m)$, second $(s)$ and ampere $(A)$. When reduced to base SI units, $1$ Henry will result into one-kilogram meter squared per second per ampere squared $(kg{m}^2{s}^{-2}{A}^{-2})$.
$\Rightarrow H={\displaystyle \frac{kg.m^2}{s^2.A^2}}$
$\Rightarrow {\displaystyle \frac{N.m}{A^2}}$
$\Rightarrow {\displaystyle \frac{kg.m^2}{C^2}}$
$\Rightarrow {\displaystyle \frac{J}{A^2}}$

Additional information:
The unit $1$ Henry is named after the American scientist Joseph Henry (the same scientist who discovered electromagnetic induction and almost at the same time as the English scientist Michael Faraday did). The inductance of a coil depends on its size, the number of turns and the permeability of the material. It is often denoted by the symbol ${}^{\prime }{H}^{\prime }$. The henry is a large unit of inductance, at various places such as audio-frequency and radio-frequency, units of millihenries$(mH)$ and microhenries $(\mu H)$ are used.

Note: Some other units related to magnetism are: Ampere for electric current, Tesla for magnetic field and Weber for magnetic flux. Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it, whose unit is Henry.