Inductance is the property of an electrical circuit that opposes any change in current. It is an inherent circuit property and depends on geometry, number of turns, area, and magnetic permeability rather than on the instantaneous value of current itself.

• Inductance plays the electromagnetic role analogous to inertia in mechanics.
• A constant current does not bring inductance into action because no changing flux-linkage effect is being produced.
• Trap: thinking larger current automatically means larger inductance. The coefficient depends on the circuit and medium, not on the current value alone.

When current in a coil changes, the flux linked with that same coil changes and induces an emf that opposes the change. This self-induced emf is called back emf and is written as e = minus L di by dt.

• The negative sign represents opposition to current change, exactly in the spirit of Lenz's law.
• The relation L = Nphi by i is the defining coefficient form when geometry remains fixed.
• Trap: using self-induction language when the changing current belongs to a different nearby coil.

The SI unit of inductance is henry, which is equivalent to weber per ampere or volt-second per ampere. Dimensional analysis shows that inductance has dimensions of M L squared T minus two A minus two.

• Henry is the practical unit used in NEET and standard circuit notation.
• Unit conversions like weber per ampere and ohm-second are common quick-check questions.
• Trap: confusing the dimensions of inductance with those of magnetic flux or emf.

Work done against self-induction while building current in a coil is stored as magnetic potential energy. The standard result is U = one-half L i squared, and the corresponding magnetic energy density form given in the text is u = B squared by 2 mu zero.

• The energy is stored in the magnetic field, not in the wire material itself as a static charge reservoir.
• The factor one-half appears because current rises from zero to its final value while the source works against the back emf.
• Trap: forgetting the square on current in energy questions.

Self-inductance formulas change with geometry: circular coil, solenoid, toroid, square coil, and coaxial-cylinder arrangements all have their own expressions. The common idea is that inductance grows with turns and favorable geometry that links more magnetic flux per unit current.

• Solenoid inductance includes permeability and cross-sectional area explicitly.
• Different geometries change how much flux linkage is created for the same current.
• Trap: memorising one solenoid formula and applying it to every coil geometry.

Mutual induction occurs when changing current in one coil changes the magnetic flux linked with a nearby coil, inducing emf in that second coil. The defining relation is N2 phi2 = M i1, and the induced emf in the secondary is written in terms of M and the rate of change of primary current.

• The source of changing flux is now a different coil, not the same coil itself.
• The coefficient M depends on turns, geometry, area, permeability, separation, orientation, and coupling.
• Trap: writing L when the induction is between two different coils.

Mutual inductance formulas depend on the paired geometry, and the most general coupling statement in the text is M = k root L1 L2 with zero less than or equal to k less than or equal to one. Maximum coupling occurs when flux produced by one coil links the other as completely as possible.

• If there is no coupling, k becomes zero and mutual inductance vanishes even when each coil may still have self-inductance.
• The value of M cannot exceed the limit set by the self-inductances and the coupling factor.
• Trap: assuming M can exist independently of self-inductance.