Storage of Electromagnetic Energy

Author: E.E. Kimberly

Switching transients in RL circuits are fundamentally caused by the storage of energy in the magnetic field of the circuit or by the release of such energy previously stored. When the circuit shown in Fig. 8-3 is closed, the power at any instant thereafter is Vi. Of that power a component I²R is converted to heat in the resistance, and the remainder P_L is stored in the magnetic field of the inductance L. The value of P_L is

Fig. 8-6. Rate of Storage of Energy by Direct Voltage Applied to an RL Circuit

By substituting in this equation the value of i from equation (8-2), we get:

(8-4)

A plot of values of this equation is shown in Fig. 8-6. The area under this curve represents the energy stored in the magnetic field of the inductance and is equal to

(8-5)

If the circuit is broken after the field has grown for any length of time t, the energy stored up to that time must be dissipated in the form of heat in the circuit resistance. The circuit resistance R_c now includes the resistance R_a (arc resistance) at the opened contacts in addition to the resistance R of the original circuit element. The energy dissipated will be divided between Ra and R in proportion to their magnitudes.

That portion dissipated at the circuit break will cause an arc. If the breaking contact points are separated by a wide gap quickly, Ra will be relatively large; and proportionately more of the energy W will appear there in the arc as heat. The faster the contact points are separated, the higher will be the voltage across the arc and so the longer will be the arc. Also, the longer the arc, the higher will be the voltage across it. For that reason the circuits of inductive devices, such as field circuits of motors and generators having large stored energy, should be opened slowly lest the insulation of the device be ruptured by high voltage induced in the winding.