A plate current of `10 mA` is obtained when 60 volts are applied across a diode tube. Assuming the Langmuir-Child equation `i_p prop V_p^(3/2)` to hold, find the dynamic resistance `r_p` in this operating condition.

Explanation

`i_p = CV_p ^(3/2) `……(1)
` di_p = 3/2 CV_(p)^(3/2-1) dv_p `
` di_p/dv_p = 3/2 CV_(p)^(1/2) ` …….(2)
` Dividing (2) and (1) `
` i/i_p di_p/dv_p = ((3//2) CV_(p)^(1/2)) /(CV_(p)^(3/2))`
` rArr (i/i_p).(di_p/dv_p) = 3/2V `
` rArr (dv_p/di_p) = 2V/3i_p `
` R = 2V/3i_p`
` = ((2 xx 60)/(3xx 10xx (10^-3)))`
` = 4 xx (10^3) = 4kW ` .