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(C) In a vacuum diode,before reaching the saturation state,the current follows the Child-Langmuir law,which states that the plate current $i_p$ is pro

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$2\sqrt{2}$

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(C) In a vacuum diode,before reaching the saturation state,the current follows the Child-Langmuir law,which states that the plate current $i_p$ is proportional to the power of the plate voltage $V_p$ (specifically $i_p \propto V_p^{3/2}$).However,in many textbook contexts for this specific problem type,it is assumed that the diode operates in the space-charge limited region where the relationship is often simplified or evaluated based on the given parameters.Given $V_1 = 400 \, V$ and $V_2 = 200 \, V$,using the relation $i \propto V^{3/2}$:$\frac{i_1}{i_2} = \left( \frac{V_1}{V_2} \right)^{3/2} = \left( \frac{400}{200} \right)^{3/2} = (2)^{3/2} = 2\sqrt{2}$.Thus,the correct ratio is $2\sqrt{2}$.

Before the saturation state of a diode,at plate voltages of $400 \, V$ and $200 \, V$,the currents are $i_1$ and $i_2$ respectively. The ratio $i_1/i_2$ will be:

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