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Question

The power delivered in the plate circular of a diode is 1.0 W when the plate voltage is 36 V. Find the power delivered if the plate voltage is increased to 49 V. Assume Langmuir-Child equation to hold.

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Solution

Given:

When plate voltage, Vp, is 36 V, power delivered in the plate circular of a diode, P, is 1.0 W.
Let the plate current be Ip.

Let the power delivered be P' and plate current be Ip' when plate voltage, Vp, is increased to 49 V

P=IpVp Ip=PVP=136
According to Langmuir-Child equation,
Ip (Vp)3/2,Ip' (Vp')3/2, IpI'p=(Vp)3/2(Vp')3/21/36Ip'=36493/2 Ip=0.04411

Thus, power delivered when the plate voltage is increased to 49 V,
P'=Vp'×Ip'P'=49×0.04411 WP'=2.1613 W=2.2 W

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