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.

Sol. P = 1 W, p = ? V base p = 36 V, V base p = 49 V, P = I base pV base p ⇒ l base p = P/V base p = 1/36 l base p ∝ (V base p)^3/2 l’ base p ∝ (V’ base p)^3/2 ⇒ l base p/l’base p = (V base p)^3/2/V’base p ⇒ 1/36/l’base p= (36/49)3/2 ⇒ 1/36/l’base p= 36/49 * 6/7 ⇒ l’base p = 0.4411 P’ = V’ base p l’ base p = 49 * 0.4411 = 2.1613 W = 2.2 W