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.

Answer 1

Given:

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

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

$$\begin{gathered} P=I_{\mathrm{p}}{V}_{\mathrm{p}} \\ \Rightarrow I_{\mathrm{p}}=\frac{P}{V_{\mathrm{P}}}=\frac{1}{36} \end{gathered}$$
According to Langmuir-Child equation,
$$\begin{gathered} I_{\mathrm{p}}\propto (V_{\mathrm{p}}{)}^{3/2}, \\ {I}_{\mathrm{p}}\text{'}\propto (V_{\mathrm{p}}\text{'}{)}^{3/2}, \\ \Rightarrow \frac{I_{\mathrm{p}}}{I{\text{'}}_{\mathrm{p}}}=\frac{(V_{\mathrm{p}}{)}^{3/2}}{(V_{\mathrm{p}}\text{'}{)}^{3/2}} \\ \Rightarrow \frac{1/36}{I_{\mathrm{p}}\text{'}}={\left(\frac{36}{49}\right)}^{3/2} \\ \Rightarrow I_{\mathrm{p}}=0.04411 \end{gathered}$$

Thus, power delivered when the plate voltage is increased to 49 V,
$$\begin{gathered} P\text{'}=V_{\mathrm{p}}\text{'}\times I_{\mathrm{p}}\text{'} \\ P\text{'}=49\times 0.04411\mathrm{W} \\ P\text{'}=2.1613\mathrm{W}=2.2\mathrm{W} \end{gathered}$$