Semiconducting Devices Question 58
Question: The relation between dynamic plate resistance (rp) of a vacuum diode and plate current in the space charge limited region, is
Options:
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}}} $
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Answer:
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}={{( \frac{i _{p}}{K} )}^{2/3}} $
Therefore $ \frac{\Delta V _{p}}{\Delta i _{p}}=\frac{2}{3{{K}^{2/3}}}i _{p}^{( \frac{2}{3}-1 )} $
Therefore $ r _{p}=(\text{constant)}I _{p}^{-1/3} $
Therefore $ r _{p}\propto \frac{1}{I _{p}^{1/3}} $
