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`.

Explanation

P = 1 W, P=?
` V_p = 36 V, V_p = 49V, `
` P = I_p V_p `
` rArr I_p= p/V_p = 1/36 `
` I_p alpha (V_(p)^(3/2)), I' alpha (V'_(p)^(3/2)), `
` rArr (I_p/I'_p)= ((V_(p)^3/2)/(V'_(p)^3/2))`
` rArr (1//36/I'_p)= (36/49)^3/2 `
`rArr 1/36I_p = 30/49 xx 6/7 `
` rArr I_p = 0.4411 `
` P' = V'_p/T'_p`
` = 49 xx 0.4411 `
` = 2.1613W = 2.2 W ` .