A plate current of 10 mA is obtained when 60 volts are applied across a diode tube. Assuming the Langmuir - child equation $i_{p} \propto V_{p}^{\frac{3}{2}}$ to hold, find the dynamic resistance $r_{p}$ in this operating condition.

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Solution

$i_{p} = C V_{p}^{\frac{3}{2}} d i_{p} = \frac{3}{2} C V_{p}^{(\frac{3}{2} - 1)} d v_{p} \frac{d i_{p}}{d v_{p}} = \frac{3}{2} C V_{p}^{\frac{1}{2}}$
Dividing (2) and (1)
$\frac{i}{i_{p}} \frac{d i_{p}}{d v_{p}} = \frac{\frac{3}{2} C V_{p}^{\frac{1}{2}}}{C V_{p}^{\frac{3}{2}}} \Rightarrow \frac{i}{i_{p}} . \frac{d i_{p}}{d v_{p}} = \frac{3}{2 V} \Rightarrow \frac{d v_{p}}{d i_{p}} = \frac{2 V}{3 i_{p}} R = \frac{2 V}{3 i_{p}} = \frac{2 \times 60}{3 \times 10 \times 10^{- 3}} = 4 \times 10^{3} = 4 k W$

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A plate current of 10 mA is obtained when 60 volts are applied across a diode tube. Assuming the Langmuir - child equation ip∝V32p to hold, find the dynamic resistance rp in this operating condition.

ip=CV32pdip=32CV(32−1)pdvpdipdvp=32CV12p Dividing (2) and (1) iipdipdvp=32CV12pCV32p⇒iip.dipdvp=32V⇒dvpdip=2V3ipR=2V3ip=2×603×10×10−3=4×103=4kW

A plate current of 10 mA is obtained when 60 volts are applied across a diode tube. Assuming the Langmuir - child equation $i_{p} \propto V_{p}^{\frac{3}{2}}$ to hold, find the dynamic resistance $r_{p}$ in this operating condition.