Lenz’s Law and current continuity

Lenz’s Law

The self-induced electromotive force e = -L * di/dt always opposes the cause that gives rise to it (Lenz’s Law): if the current increases, the coil slows down its rise; if it decreases, the coil tends to maintain it. The coil is thus often described as having ‘electrical inertia’, by analogy with mass in mechanics.

Continuity of current

Fundamental consequence: the current flowing through a coil cannot, in practice, be discontinuous. A discontinuity in i would result in an infinite di/dt, and therefore an infinite voltage u, which is physically impossible in a real circuit. We write:

i(0-) = i(0+)

Comparison: coil vs capacitor

Quantity	Coil (L)	Capacitor (C)
Current i	continuous (does not jump)	may be discontinuous
Voltage u	may be discontinuous	continuous (does not jump)
Time constant	τ = L/R	τ = R*C

Example

When an inductive circuit (relay coil, motor) is abruptly opened, the current cannot be cancelled out instantly: it seeks another path, producing a voltage spike across the switch terminals, visible as a spark. This is why a free-wheeling diode is connected in parallel across the relay coils.

Common pitfall

Do not confuse ‘current continuity’ (characteristic of the coil) with ‘voltage continuity’ (characteristic of the capacitor): they are exact opposites, and this is a very common mistake in exams.