The power delivered in the plate circuit 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

$P - 1 W, P = ? V_{p} = 36 V, V_{p} = 49 V, P = I_{p} V_{p} \Rightarrow I_{p} = \frac{P}{V_{P}} = \frac{1}{36} I_{p} α (V_{p})^{\frac{3}{2}}, I^{'} α (V_{p}^{'})^{\frac{3}{2}} \Rightarrow \frac{I_{p}}{I_{p}^{'}} = \frac{(V_{p})^{\frac{3}{2}}}{(V_{p}^{'})^{\frac{3}{2}}} \Rightarrow \frac{\frac{1}{36}}{I_{p}^{'}} = {(\frac{36}{49})}^{\frac{3}{2}} \Rightarrow I_{p} = 0.4411 P^{'} = \frac{V_{p}^{'}}{T_{p}^{'}} = 49 \times 0.4411 = 2.1613 W = 2.2 W$

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The power delivered in the plate circuit 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.

P−1W,P=?Vp=36V,Vp=49V,P=IpVp⇒Ip=PVP=136Ipα(Vp)32,I′α(V′p)32⇒IpI′p=(Vp)32(V′p)32⇒136I′p=(3649)32⇒Ip=0.4411P′=V′pT′p=49×0.4411=2.1613W=2.2W