The relation between dynamic plate resistance $(r_{p})$ of a vacuum diode and plate current in the space charge limited region, is

r_{p} \propto I_{p}

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r_{p} \propto I_{p}^{3 / 2}

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r_{p} \propto \frac{1}{I_{p}}

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r_{p} \propto \frac{1}{{(I_{p})}_{p}^{1 / 3}}

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Solution

The correct option is D $r_{p} \propto \frac{1}{{(I_{p})}_{p}^{1 / 3}}$
The dynamic plate resistance is $r_{p} = \frac{Δ V_{p}}{Δ i_{p}}$
Now for a vacuum diode $i_{p} = K_{p}^{- 3 / 2} \Rightarrow= V_{p} = {(\frac{i_{p}}{K})}^{2 / 3}$

$\Rightarrow \frac{Δ V_{p}}{Δ i_{p}} = \frac{2}{3 K^{2 / 3}} \times \frac{1}{i_{p}^{⎛ ⎝ \frac{2}{3} - 1 ⎞ ⎠}}$

$\Rightarrow r_{p} = (c o n s t a n t) I_{p}^{- 1 / 3} \Rightarrow r_{p} \propto \frac{1}{{(I_{p})}_{p}^{1 / 3}}$

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The relation between dynamic plate resistance (rp) of a vacuum diode and plate current in the space charge limited region, is

The correct option is D rp∝1(Ip)1/3The dynamic plate resistance is rp=ΔVpΔipNow for a vacuum diode ip=K−3/2p⇒=Vp=(ipK)2/3⇒ΔVpΔip=23K2/3×1i⎛⎝23−1⎞⎠p⇒rp=(constant)I−1/3p⇒rp∝1(Ip)1/3

The relation between dynamic plate resistance $(r_{p})$ of a vacuum diode and plate current in the space charge limited region, is