Power cuts and power surges

Abrupt disconnection of the circuit

When the switch in an RL circuit carrying a current I₀ = E/R is opened, the coil resists the abrupt cessation of the current: the current cannot drop to zero instantly (continuity of current in an inductor).

Modelling after disconnection

If the disconnection introduces a resistance R’ allowing the current to continue flowing in a closed loop, the equation becomes:

0 = (R + R') * i(t) + L * di/dt, where i(0) = E/R

The solution is: i(t) = (E/R) * exp(-t/tau'), where tau' = L/(R + R')

Overvoltage

The voltage across the coil (or the switch) is u_L = -L*di/dt and can become very high. If the circuit is opened abruptly with no return path (R’ → ∞), the coil generates a theoretically very high overvoltage, which produces a destructive electric arc (a spark when a switch is opened).

Practical application

This is the principle used in automotive ignition coils or spark gaps: this overvoltage is utilised to generate a spark. Conversely, electronic circuits (relays, coils) are protected by a free-wheeling diode connected in anti-parallel across the coil, to clip this overvoltage and protect the components.

Common pitfall

Do not confuse sudden opening (destructive overvoltage) with controlled decay (via a discharge resistor or a diode). The stored energy must always be dissipated somewhere: either as Joule heating in R’, or in the electric arc.