Module 2 : Gaseous Dielectrics
Lecture 10 : Breakdown in Uniform Fields (Paschen's Law)

Breakdown Voltage Characteristics in Uniform Fields (Paschen's Law)   (contd. )

  • It is more convenient to introduce the 'relative gas density',  δ - a dimensionless quantity, in place of gas pressure p. ' δ' takes care of the effect of temperature on the mean free path of electrons in the gas at constant pressure. The number of collisions made by an electron in crossing a gap is, therefore, proportional to the product δd and . Correction for the variation in ambient conditions of air is made by introducing the 'relative air density', δ, defined as,
                                                                                                                                                      (10.4)

where p is in Torr and t in °C.

At normal temperature (t = 20°C) and pressure (p = 760 Torr), δ is equal to one. Equation for normal temperature and pressure will be,

                                                                                                                        (10.5)

It is interesting to note that even in uniform field at constant pressure and temperature, the electric strength of air is not constant. It tends to 24 kV /cm for very long gaps. The value 31 kV/cm is applicable only for d = 1, that is for one cm gap at 760 Torr and 20°C. For gaps of a few mm, the electric strength is much higher than 31 kV/cm. It has been measured to rise to about 92 kV/cm for a gap of 0.1 mm. A plot of Equation 10.5 is shown in Fig. 6.3. This is representing the breakdown characteristic of atmospheric air at normal temperature and pressure in uniform fields. The electric strength value 31 kV/cm, measured across one cm gap in uniform field at normal temperature and pressure, is known as the 'inherent' or 'intrinsic strength' of air Ebi. For longer gap lengths in uniform fields, the electric strength of air reduces to about 25 kV/cm, where a breakdown with streamer mechanism is more likely to develop.

 
Fig  10.3  Breakdown voltage characteristics of atmospheric air in uniform fields.