Chapter 2: Conduction and Breakdown in Gases

Example 1: pg 64

In [1]:
#example 2.1
#calculation of breakdown strength of air

#given data
d1=0.1#length(in cm) of the gap
d2=20#length(in cm) of the gap

#calculation
#from equation of breakdown strength
E1=24.22+(6.08/(d1**(1./2)))#for gap d1
E2=24.22+(6.08/(d2**(1./2)))#for gap d2
#results
print 'the breakdown strength of air for 0.1mm air gap is (kV/cm.) = ',round(E1,2)
print '\nthe breakdown strength of air for 20 cm air gap is (kV/cm.) = ',round(E2,3)

the breakdown strength of air for 0.1mm air gap is (kV/cm.) =  43.45

the breakdown strength of air for 20 cm air gap is (kV/cm.) =  25.58

Example 2: pg 64

In [2]:
#example 2.2
#calculation of Townsend primary ionization coefficient
from math import log
#given data
d1=0.4#gap distance(in cm)
d2=0.1#gap distance(in cm)
I1=5.5*10**-8#value of current(in A)
I2=5.5*10**-9#value of current(in A)

#calculation
#from equation of current at anode I=I0*exp(alpha*d)
alpha=(log(I1/I2))*(1/(d1-d2))
#results
print 'Townsend primary ioniztion coefficient is (/cm torr) = ',round(alpha,3)

Townsend primary ioniztion coefficient is (/cm torr) =  7.675

Example 3: pg 65

In [3]:
#example 2.3
#calculation of Townsend secondary ionization coefficient
from math import exp
#given data
d=0.9#gap distance(in cm)
alpha=7.676#value of alpha

#calculation
#from condition of breakdown.....gama*exp(alpha*d)=1
gama=1/(exp(d*alpha))
#results
print '%s %.3e' %('the value of Townsend secondary ionization coefficient is ',gama)

the value of Townsend secondary ionization coefficient is  9.994e-04

Example 4: pg 65

In [2]:
#example 2.4
#calculation of breakdown voltage of a spark gap
from math import log
#given data
A=15.#value of A(in per cm)
B=360.#value of B(in per cm)
d=0.1#spark gap(in cm)
gama=1.5*10**-4#value of gama
p=760.#value of pressure of gas(in torr)

#calculation
#from equation of breakdown voltage
V=(B*p*d)/(log((A*p*d)/(log(1+(1/gama)))))

#results
print 'the value of breakdown voltage of the spark gap is (V) = ',round(V)
print 'The answer is a bit different due error in textbook'

the value of breakdown voltage of the spark gap is (V) =  5626.0
The answer is a bit different due to rounding off error in textbook

Example 5: pg 65

In [4]:
#example 2.5
#calculation of minimum spark over voltage
from math import log
#given data
A=15.#value of A(in per cm)
B=360.#value of B(in per cm)
gama=10**-4#value of gama
e=2.178#value of constant

#calculation
Vbmin=(B*e/A)*(log(1+(1/gama)))

#results
print 'the value of minimum spark over voltage is (V) = ',round(Vbmin)
print 'The answer is a bit different due error in textbook'

the value of minimum spark over voltage is (V) =  481.0
The answer is a bit different due error in textbook