With the help of $L = \frac{N\phi}{I}$ and $\varepsilon = -L\frac{dI}{dt}$,give two definitions of self-inductance.

(N/A) The total magnetic flux linked with a coil of $N$ turns carrying current $I$ is given by $N\phi = LI$,where $L$ is the self-inductance of the coil.
$1$. From the relation $L = \frac{N\phi}{I}$,if $I = 1 \text{ A}$,then $L = N\phi$. Thus,self-inductance is defined as the total magnetic flux linked with the coil per unit current flowing through it.
$2$. From the relation $\varepsilon = -L\frac{dI}{dt}$,if $\frac{dI}{dt} = 1 \text{ A/s}$,then $|\varepsilon| = L$. Thus,self-inductance is defined as the magnitude of the self-induced electromotive force (emf) produced in the coil per unit rate of change of current in the circuit.
The $SI$ unit of self-inductance is Henry $(H)$,which is equivalent to $Wb/A$ or $Vs/A$. Its dimensional formula is $[M^1 L^2 T^{-2} A^{-2}]$.