With the help of L =`(Nphi)/I` and `epsilon=-L(dI)/(dt)` give two definitions of self inductance.

Explanation

Total flux linked with a coil of N turns carrying current I is given by `Nphi` = LIy where L is called the self-inductance of the coil.
`therefore` From `L=(N phi)/I`, if I=1A , then L=`Nphi`
From this equation, "The total flux per unit current passing through coil is defined as self inductance".
Self induced emf is given by `epsilon=-L(dI)/(dt)` when `(dI)/(dt)`=I unit then `epsilon=-L` . So the self-inductance of a circuit can be defined as under :
"The self induced emf produced per unit rate of change of the current in the circuit is called self inductance of the circuit".
Self-inductance unit is Vs/A or H or `Omegas` or Wb/A, its dimensional formula is `[M^1 L^2 T^(-2) A^(-2)]`.