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Question
The power delivered in the plate circular of a diode is 1.0 W when the plate voltage is 36 V. Find the power delivered if the plate voltage is increased to 49 V. Assume Langmuir-Child equation to hold.
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Solution
Given:-
When plate voltage, Vp, is 36 V, power delivered in the plate circular of a diode, P, is 1.0 W.
Let the plate current be Ip.
Let the power delivered be P' and plate current be Ip' when plate voltage, Vp, is increased to 49 V
\[ P = I_p V_p \]
\[ \Rightarrow I_p = \frac{P}{V_P} = \frac{1}{36}\]
According to Langmuir-Child equation,
\[I_p \propto ( V_p )^{3/2} , \]
\[ I_p ' \propto ( V_p ' )^{3/2} , \]
\[ \Rightarrow \frac{I_p}{I '_p} = \frac{( V_p )^{3/2}}{( V_p ' )^{3/2}}\]
\[ \Rightarrow \frac{1/36}{I_p '} = \left( \frac{36}{49} \right)^{3/2} \]
\[ \Rightarrow I_p = 0 . 04411\]
Thus, power delivered when the plate voltage is increased to 49 V,
\[P' = V_p ' \times I_p '\]
\[P' = 49 \times 0 . 04411 W\]
\[P' = 2 . 1613 W = 2 . 2 W\]
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