Actuators

These devices convert electromagnetic energy to mechanical energy to produce intermittent mechanical movement (e.g. opening a valve in a central heating system or controlling the inlet of water in a washing machine).

We have already noted that the inductance of a coil is defined as the flux linkage (Nφ) per unit current, i.

hence back emf

V(t)=NdØ/dt

Solving the magnetic circuit problem allows φ to be expressed as a function of i.Hence we may write the back emf in terms
of the current in the coil instead of φ and  the constants then involved are grouped and termed the self inductance of the coil,
L  (Henrys).

V(t)=NdØ/dt =Ldi/dt

The energy stored in the magnetic field has also been considered previously. The circuit considered consisted of an inductor and resistor in series, connected to a voltage supply via a switch. Initially, the switch is open and there is no current flowing in the circuit and hence no magnetic field in the coil. If the switch is closed at t=0, the current builds up with
time as the applied voltage gradually overcomes the back emf generated in the coil, trying to prevent the change in current. As the current increases, more and more energy is stored in the magnetic field in the inductor. We have the total energy delivered by the supply since t=0 to be:

The first term is the energy dissipated in the resistor and is 'lost' as heat. The second term is the energy stored in the inductor (in its magnetic field).

If L were now to change (for example by moving the magnetic plunger in or out of a gap in the coil former), then conservation of energy dictates that the change in the electrical energy stored in the magnetic field equals the work done in moving the magnetic material in or out of the core. This is the basis of the electric solenoid actuator.