The first ionisation coefficient for a gas is approximately given by $? = A p e^{\frac{? Bp}{E}}$ , where $p$ is the pressure in $mm$ . Hg and $E$ is electric field in V/cm. Paschen's curve for this gas is given in Figure 1.4. Suppose the second ionisation coefficient for this gas is $? = 0.01$ . 1.1 Calculate the constants $A$ and $B$ . 1.2 Calculate the electrode separation, $d$ , if $p = 50 mm . Hg$ and $E = 4 kV / cm$ . [Hint: Differentiate the expression for breakdown voltage, $V_{B D}$ , with respect to pd and equate it to zero.]

Question

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The first ionisation coefficient for a gas is approximately given by

? = A p e^{\frac{? Bp}{E}}

, where

p

is the pressure in

mm

. Hg and

E

is electric field in V/cm. Paschen's curve for this gas is given in Figure 1.4. Suppose the second ionisation coefficient for this gas is

? = 0.01

. 1.1 Calculate the constants

A

and

B

. 1.2 Calculate the electrode separation,

d

, if

p = 50 mm . Hg

and

E = 4 kV / cm

. [Hint: Differentiate the expression for breakdown voltage,

V_{B D}

, with respect to pd and equate it to zero.]

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