Paschen's law Is an equation that gives the breakdown voltage, that is, the voltage necessary to start a discharge or electric arc, between two electrodes in a gas as a function of pressure and gap length. It is named after Friedrich Paschen who discovered it empirically in 1889. Paschen studied the breakdown voltage of various gases between parallel metal plates as the gas pressure and gap distance was varied:

1. Paschen's Law
And Electrical Discharge
Prepared By :
Mohanad Hameed Mahmood

2. Introduction
Paschen's law Is an equation that
gives the breakdown voltage, that is,
the voltage necessary to start a
discharge or electric arc, between
two electrodes in a gas as a function
of pressure and gap length. It is
named after Friedrich Paschen who
discovered it empirically in 1889.

3. PASCHEN'S LAW
Paschen studied the breakdown voltage of various
gases between parallel metal plates as the gas
pressure and gap distance were varied:
• With a constant gap length, the voltage necessary to
arc across the gap decreased as the pressure was
reduced and then increased gradually, exceeding its
original value.
• With a constant pressure, the voltage needed to
cause an arc reduced as the gap size was reduced
but only to a point. As the gap was reduced further,
the voltage required to cause an arc began to rise
and again exceeded its original value.

4. Paschen's Law:
“At constant temperature in a uniform field the
sparking potential of gas depend only upon the
product of gas pressure and electrode spacing
P.d” .
For breakdown:
_________(1)
As α is a function of pressure p and the ratio so:
________(2)

5. And is a function of the ratio
So: ______________(3)
For uniform field at breakdown:
Vs : Breakdown voltage
∴ 𝑬𝒔 =
𝑽𝒔
𝒅𝒔
…(4) Sub in (2) and (3) and then sub all in (1)
∴

6. Then we may write the sparking voltage Vs as a function of p
and d
This relation Vs = f(P.d) is known as paschen’s law.
The breakdown voltages for uniform field gap in gases at
different pressures may therefore be plotted in the form of
curves relating the sparking voltage VB(Vs) with the
production of gap distance (d) and gap pressure (p)

7. This table gives the breakdown voltage for some gases

8. Electrical Discharges in Non- Uniform Fields:
 when electric field is established between two similar
electrodes (except that point-point electrodes which have non-
uniform field) the field is said to be uniform.
 The main feature of the uniform field is that the field lines
between the electrodes are homogeneous and has a uniform
intensity distribution.
HV
Sphere - sphere Plane - planefig (1): uniform fields

9.  On the other hand different electrodes have non-uniform
field establish between them when a voltage is applied in
this case the field has unequal intensity distribution in the
space between electrodes .
Point - sphere Point - plane
HV
fig (2):
Non_ uniform fields

10.  When we have two similar electrodes (plane-plane) the filed
intensity has its maximum value at the electrode surface and
minimum in the middle of the space as shown in the fig.(3).
Plane - plane
HV
fig (3): uniform fields

11.  For different electrode shapes (point-plane) the greatest field
intensity occurs on the surface of the electrode of smaller
radius of curvature while the region of minimum intensity is
shifted to the opposite electrode as shown in fig.(4)
Point - plane
HV
fig (4): Non_ uniform fields

12. When the field is non-uniform then the field in the region
of highest stress may exceed the breakdown strength of the
gas and cause a localized glow discharge known as corona
Fig (4): Corona effect

13. Note:
The electric field associated with high voltage system are
generally non-uniforms .
The phenomena occurs when the ratio between the
maximum field Emax and the average field Eav
exceeds ratio 5:1 this ratio is called field factor (K)
K=1 for uniform field

14. Discharge Characteristics in Non-Uniform Fields
1. Negative polarity
• Consider a point - plane gap as shown in the fig(5) with negative high
voltage applied to the point electrode.
• Positive ions formed by the field bombarded the electrodes and release
electrons.
• These electrons produce electron avalanches which sustain the discharge,
leave behind a positive space charge and flow towards the anode.
• They migrate into regions of weaker field they slow down and form negative
ions by attachment.
• The positive ions are withdrawn from the field into point.
• The negative ions rapidly accumulate where the field decreasing and cause
reduction in the field.

15. • Shortens the effective high field region to such an extent
that electrons cannot be accelerated sufficiently to produce
ionization and the discharge is chocked off.
Cathode
Anode
- HV
+Hv
point
plane
+o
-oe
Fig(5):Negative
polarity

16. 2-Positive Polarity:
• Positive high voltage is applied to the point (electrode) .
• The electrons are accelerated by the field and move towards
the highly stressed electrode across the gap they cause
electron avalanche and leave behind positive ions.
• This positive charge acts as an extension to the electrode
creates an intense field and leads to secondary avalanche.
• These avalanche sustain the discharge.
• The positive ions move away into weaker field and slow
down on arriving the plane electrode .

17. Note:
Number of electrons moving in the field near the
electrode in positive polarity is much greater than
with negative polarity and therefore the energy
and the amplitude of positive corona is greater
than the negative corona.