Regarding self-inductance :
A : The self-inductance of the coil depends on its geometry.
B : Self-inductance does not depend on the permeability of the medium.
C : Self-induced e.m.f. opposes any change in the current in a circuit.
D : Self-inductance is the electromagnetic analogue of mass in mechanics.
E : Work needs to be done against self-induced e.m.f. in establishing the current.
Choose the correct answer from the options given below:

Let's analyze each statement regarding self-inductance:

(A) The self-inductance of the coil depends on its geometry.  True
Self-inductance ($L$) depends on factors like the number of turns, length, cross-sectional area, and shape of the coil.

(B) Self-inductance does not depend on the permeability of the medium.  False
The self-inductance of a coil is given by $L = \mu N^2 A / l$, where $\mu$ is the permeability of the medium. A higher permeability ($\mu$) increases inductance.

(C) Self-induced e.m.f. opposes any change in the current in a circuit.  True
According to Lenz’s Law, the self-induced emf opposes the change in current that caused it.

(D) Self-inductance is the electromagnetic analogue of mass in mechanics.  True
Just as mass resists acceleration in mechanics (Newton’s second law), self-inductance resists changes in current ($V = L \frac{dI}{dt}$), making it an electromagnetic analogue of inertia.

(E) Work needs to be done against self-induced e.m.f. in establishing the current.  True
Since self-inductance resists changes in current, energy must be supplied to overcome this opposition and establish the current.

Final Answer:

✔ Correct statements: A, C, D, E
✖ Incorrect statement: B