Electronic Devices Question 254

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}}} $

Show Answer

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}} $



NCERT Chapter Video Solution

Dual Pane