# Inductance of a Coil

Inductance of a coil In addition to the electric fields that occur, for instance, between the plates of a charged capacitor, electrical engineering also relies on a second kind of field, magnetic fields. While electric fields are generated by static charge, magnetic fields are generated by moving charge carriers, i.e. electric current. If an electric current passes through a coil comprising an array of conductive windings, magnetic field lines run through the coil as a result. The magnetic field's intensity is represented by the magnetic flux. If the flux through the coil changes (e.g. by varying the current), a self-induced voltage is generated in the coil. The intensity of this voltage depends on the rate of change of current as well as the size and nature of the coil. The coil's inductance L is a measure of its ability to generate self-induced voltages. The following relationship applies to extended coils: µ0 is the magnetic field constant, µr the relative permeability of the material in the core of the coil, N the number of windings, l the length of the coil and A its cross-section (see the diagram below). The unit of inductance is the Henry (H, 1 H = 1 Vs/A). A coil has an inductance of 1 H if a constant change of 1 A per second in the current flowing through a coil results in a self-induced voltage of 1 V. Energising and de-energising a coil If direct current is passed through a coil, the current characteristic after a brief transient phase is constant, so that no voltage is self-induced. In this case, the coil acts as an ohmic load, the (usually very low) resistance of which depends on the coil material's specific resistivity as well as the length and cross-section of the coil wire. When a coil is energised, its magnetic field builds up. The resulting change in flux gives rise to a self-induced voltage in the opposite direction to the applied voltage. Consequently, the current in the electric circuit does not rise abruptly (as in the case of a resistive load). Instead, it rises very gradually to a final value. The reverse process takes place on de-energisation of the coil. The decaying magnetic field now produces a self-induced voltage acting in the same direction as the previously applied voltage and capable of assuming very large values in coils with strong magnetic fields. The self-induced voltage tends to sustain the current through the coil, so that the current does not cut off suddenly, instead gradually dropping to zero. The diagrams below demonstrate the de-energising process. In the active state (left-hand illustration), a current I flows through the coil L. If the electric circuit is then broken (right-hand illustration), the energy stored within the coil's magnetic field tends to sustain the current. Because the current can no longer flow via the voltage source, it takes a detour via the resistor RL connected in parallel with the coil. In this process, the energy of the magnetic field is converted into thermal energy, causing the current to decay rapidly. The decay characteristic, as in the case of the capacitor, is exponential. The time constant in this case is the quotient of the inductance and the ohmic resistance. The absence of a resistor RL would result in a very high voltage peak, easily capable of damaging sensitive components (e.g. in integrated circuits). For this reason, in practice inductors are usually connected in parallel with free-wheeling diodes which short-circuit voltage peaks across the coil to ensure that the coil's electromagnetic energy is converted into thermal energy.