Using Townsend's second ionization criterion, consider I, = 4 × 107 A. Consider a 2.28/cm. If y = 0.0075, find the gap spacing dspark in cm for spark breakdown criterion.

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Using Townsend's second ionization criterion, consider I, = 4 × 107 A. Consider a =
2.28/cm. If y = 0.0075, find the gap spacing dspark in cm for spark breakdown criterion.
Transcribed Image Text:Using Townsend's second ionization criterion, consider I, = 4 × 107 A. Consider a = 2.28/cm. If y = 0.0075, find the gap spacing dspark in cm for spark breakdown criterion.
Expert Solution
Step 1

Given:

I0=4×10-7 A

Townsend's primary ionization coefficient, α=2.28/cm

Townsend's secondary ionization coefficient, γ=0.0075

 

Step 2

The current is given by,

I=I0×eαdI-γeαd-1

 

At the spark breakdown, I become infinity which would be possible only if the denominator becomes zero.

1-γeαdspark-1=0

On rearranging,

γeαdspark-1=1

 

On further rearranging,

eαdspark-1=1γ

Substituting the values of α=2.28/cm and γ=0.0075,

e2.28dspark-1=10.0075

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