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Electric Current through Gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsElectric Current through Gases4 Marks
Question
The plate current in a triode can be written as $\text{i}_\text{p}=\text{k}\Big(\text{V}_\text{g}+\frac{\text{V}_\text{p}}{\mu}\Big)^{\frac{3}{2}}$ Show that the mutual conductance is proportional to the cube root of the plate current.
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Answer

$\text{i}_\text{p}=\text{k}\Big(\text{V}_\text{g}+\frac{\text{V}_\text{p}}{\mu}\Big)^{\frac{3}{2}}\ ....(\text{i})$Diff. the equation,
$\text{di}_\text{p}=\text{K}\frac{3}{2}\Big(\text{V}_\text{g}+\frac{\text{V}_\text{p}}{\mu}\Big)^{\frac{1}{2}}\text{dV}_\text{g}$
$\frac{\text{di}_\text{P}}{\text{dV}_\text{g}}=\frac{3}{2}\text{K}\Big(\text{V}_\text{g}+\frac{\text{V}_0}{\mu}\Big)^{\frac{1}{2}}$
$\text{g}_\text{m}=\frac{3}{2}\text{K}\Big(\frac{\text{V}_\text{g}+\text{V}_\text{p}}{\mu}\Big)^{\frac{1}{2}}\ ....(\text{ii})$
From (i) $\text{i}_\text{p}=\text{k}'(\text{gm})^{3}$
$\text{g}_\text{m}\propto3\sqrt{\text{i}_\text{p}}$

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