With the aid of a suitable diagram to aid your explanation show that for a linear non- saturated magnetic system…

With the aid of a suitable diagram to aid your explanation show that for a linear non- saturated magnetic system comprising of a coil carrying some current I the energy stored in the magnetic system W is
W 1 LI 2 2
Now draw a typical electromagnetic simple relay actuator arrangement showing the soft iron moving armature position of the coil airgap and return spring. Moreover give an explanation as to how the relay functions.
A particular simple relay has a coil of N = 1200 turns a cross sectional area of the soft iron A = 100mm2 and airgap length X = 5mm when the armature is in the open position and X = 2mm when the armature is in the closed position. If the spring which keeps the relay contacts open has a spring constant of 1Nm show how the current to close the coil may be calculated and give the current level. Furthermore show the calculation which then gives the current at which the relay opens stating the current level.
Explain why the current levels to close and open the contacts are not equal and explain how this may be of benefit to the correct operation of the relay.
A transistor switch is used to energise the simple relay from a 48 V supply (Vs). The relay possesses a coil resistance of R = 30 and an inductance of L = 0.06 H as shown electrically in Figure 1. The relay switches on for currents of 0.5 A or greater but does not switch off until the current has fallen below 0.2 A or less. The transistor is controlled by the drive voltage vB and you should assume that the transistor and the diode exhibits the ideal characteristics of instantaneous switching and zero on-state voltage drop. The transistor T is protected from the effects of energy stored in the relay inductance by the diode resistor network D-Rs.
Figure 1 Relay driver
Using MATLAB or LTSpice show the waveforms for the relay current iL transistor collector current iC and diode current iD that you would expect to see if the transistor is driven by a square-wave control voltage vB that is of sufficient duration for the currents to settle to their target levels after a switching event. Assume Rs = 0 and there is no movement from the relay armature.
Determine the time delay between the transistor T switching on and the relay’s response action. Assume that T had been off for a long period before the switch on event.
Find the time delay between the transistor T switching off and the relay’s response action. Assume that T had been on for a long period before the switch off event and that Rs = 0 .
Determine the value of Rs that should be included in series with D to make the answer above equal to 2 ms.
Using your solution above determine the minimum collector-emitter voltage vCE rating that T should have if resistor Rs is included. Sketch the waveform you would expect to see for vCE under these conditions. Show at least one complete period of the control voltage vB.