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Electric Current through Gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsElectric Current through Gases4 Marks
Question
Two discharge tubes have identical material structures and the same gas is filled in them. The length of one tube is 10cm and that of the other tube is 20cm. Sparking starts in both the tubes when the potential difference between the cathode and the anode is 100V. If the pressure in the shorter tube is 1.0mm of mercury, what is the pressure in the longer tube?
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Answer

$\text{V}=\text{f(Pd)}$$\text{V}_\text{s}=\text{P}_\text{s}\text{d}_\text{s}$
$\text{V}_\text{L}=\text{P}_\text{L}\text{d}_\text{L}$
$\Rightarrow\frac{\text{V}_\text{s}}{\text{V}_\text{L}}=\frac{\text{P}_\text{s}}{\text{P}_\text{L}}\times\frac{\text{d}_\text{s}}{\text{d}_\text{L}}$
$\Rightarrow\frac{100}{100}=\frac{10}{20}\times\frac{1\text{mm}}{\text{x}}$
$\Rightarrow\text{x}=\frac{1\text{mm}}{2}=0.5\text{mm}$

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