Q. The relation between dynamic plate resistance $(r_{p})$ of a vacuum diode and plate current in the space charge limited region, is
A) $r_{p} \propto I_{p}$
B) $r_{p} \propto I_{p}^{3/2}$
C) $r_{p} \propto \frac{1}{I_{p}}$
D) $r_{p} \propto \frac{1}{\left( I_{p} \right)^{1/3}}$
Explanation
(d) The dynamic plate resistance is $r_{p} = \frac{\mathrm{\Delta}V_{p}}{\mathrm{\Delta}i_{p}}$
Now for a vacuum diode $i_{p} = KV_{p}^{3/2} \Rightarrow V_{p} = \left( \frac{i_{p}}{K} \right)^{2/3}$
$\Rightarrow \frac{\mathrm{\Delta}V_{p}}{\mathrm{\Delta}i_{p}} = \frac{2}{3K^{2/3}}i_{p}^{\left( \frac{2}{3} - 1 \right)}$
$\Rightarrow r_{p} = (constant)i_{p}^{- 1/3} \Rightarrow r_{p} \propto \frac{1}{I_{p}^{1/3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.