Inductance and Inductors
Inductance defined
Inductance is the property of a circuit that opposes a change of current by producing a back emf. L = NΦ/I, in henries. The back emf is e = −L di/dt: the faster the current changes, the larger the emf. This is why interrupting an inductive circuit produces a large spark, and why suppression diodes and RC snubbers are fitted across relay and motor coils.
Self-inductance is a coil's own effect; mutual inductance is coupling between two coils sharing flux, the basis of the transformer. A common iron core improves coupling.
Energy, series and parallel
Energy stored W = ½LI². Inductors in series add (no mutual coupling); in parallel they combine like resistors: 1/L = 1/L₁ + 1/L₂.
Time constant for an L-R circuit: τ = L/R. Current rises to 63% of final after one τ and is effectively established after five. In steady state an ideal inductor is a short circuit to DC.
Factors affecting L
L = µ₀µ_r N²A/l: more turns, greater core area and higher permeability raise inductance; greater length reduces it. An air gap lowers inductance but raises the saturation limit and stability, which is why DC-carrying filter chokes often have one.
Traps
- Inductors oppose change in current; capacitors oppose change in voltage.
- At DC steady state an inductor is a short and a capacitor is an open circuit.
- Series/parallel rules for inductors mirror resistors - the opposite of capacitors.
- Interrupting an inductive circuit creates a high voltage hazard.
Worked example
An L-R circuit with L = 0.5 H and R = 100 Ω: τ = 0.005 s = 5 ms, so the current is essentially steady after about 25 ms.