A) \[{{r}_{p}}\propto {{I}_{p}}\]
B) \[{{r}_{p}}\propto I_{p}^{3/2}\]
C) \[{{r}_{p}}\propto \frac{1}{{{I}_{p}}}\]
D) \[{{r}_{p}}\propto \frac{1}{{{({{I}_{p}})}^{1/3}}}\]
Correct Answer: D
Solution :
The dynamic plate resistance is \[{{r}_{p}}=\,\frac{\Delta {{V}_{p}}}{\Delta {{i}_{p}}}\] Now for a vacuum diode \[{{i}_{p}}=KV_{p}^{3/2}\,\Rightarrow \,{{V}_{p}}={{\left( \frac{{{i}_{p}}}{K} \right)}^{2/3}}\] Þ \[\frac{\Delta {{V}_{p}}}{\Delta {{i}_{p}}}=\frac{2}{3\,{{K}^{2/3}}}i_{p}^{\left( \frac{2}{3}-1 \right)}\] Þ \[{{r}_{p}}=(\text{constant)}\,I_{p}^{-1/3}\] Þ \[{{r}_{p}}\propto \frac{1}{I_{p}^{1/3}}\]
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