When 60 volts are applied across a diode tube, a plate current of 10 mA is obtained. Assuming that the Langmuir–Child equation i_p V_p^ 3/2 is valid, determine the dynamic resistance r_p in this operating condition.

Step-by-step solution

According to the Langmuir-Child equation, the plate current is given by: i_p = k V_p^ 3/2 Differentiating with respect to V_p , we get: di_p dV_p = 3 2 k V_p^ 1/2 Multiplying and dividing by V_p gives: di_p dV_p = 3 2 k V_p^ 3/2 V_p = 3 2 i_p V_p The dynamic resistance r_p is the reciprocal of this derivative: r_p = dV_p di_p = 2 3 V_p i_p Substituting the given values V_p = 60 V and i_p = 10 mA = 10 10⁻³ A : r_p = 2 3 60 10 10⁻³ r_p = 2 3 6000 = 4000