Two discharge tubes possess identical material structure and are filled with the same gas. The length of one tube is 10 cm while that of the second tube is 20 cm . Sparking initiates in both tubes when the potential

Question

Quantrex Academy · Accepted Answer

Correct answer: C. 0.5 mm of mercury

According to Paschen's law, the sparking potential

V

of a gas between two electrodes depends only on the product of the gas pressure

p

and the distance

d

between the electrodes.

V = f(pd)

Since the sparking potential is the same for both tubes, the product of pressure and length must be constant.

p_1 d_1 = p_2 d_2

Substituting the given values

p_1 = 1.0 \text{ mm}

of Hg,

d_1 = 10 \text{ cm}

, and

d_2 = 20 \text{ cm}

:

1.0 \times 10 = p_2 \times 20

p_2 = \dfrac{10}{20} = 0.5 \text{ mm}

of Hg

Two discharge tubes possess identical material structure and are...

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