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What is the plate current in a diode valve under the space charge limited operation, when the plate potential is 60 V? In a diode valve, the plate current is 320 mA, when the plate potential is 240 volts:\begin{align} & a)30mA \\ & b)20mA \\ & c)40mA \\ & d)10mA \\ & \\ \end{align}

Last updated date: 20th Sep 2024
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Hint: As the given question is related to planar diode, child-Langmuir law can be used to find the relation between current and voltage in a planar diode. Space charge is a concept in which excess electric charge is treated as a continuum of charge distributed over a region of space. Using this law, we can find the current at particular voltage.
Formulas used:
$I\alpha {{V}^{\dfrac{3}{2}}}$

We were given the value of voltage at certain current. Now, we need to find the value of current at some other voltage.
$\dfrac{{{I}_{1}}}{{{I}_{2}}}={{(\dfrac{{{V}_{1}}}{{{V}_{2}}})}^{\dfrac{3}{2}}}$
Substituting the values in the above formula we get,
\begin{align} & \dfrac{I}{320}={{(\dfrac{60}{240})}^{\dfrac{3}{2}}} \\ & I=\dfrac{320}{8}=40mA \\ \end{align}

Therefore, the correct option is option c.