For a 6F6 triode tube, the plate current, plate voltage, and grid voltage are related by i_p = 41(V_p + 7 V_g)^ 1.41 , where V_p and V_g are in volts and i_p is in microamperes. If the tube is operated at V_p = 250 V and V_g = -20 V , calculate the plate resistance.

Step-by-step solution

The plate current is given by: i_p = 41(V_p + 7 V_g)^ 1.41 A The plate resistance r_p is defined as the reciprocal of the partial derivative of plate current with respect to plate voltage at a constant grid voltage: r_p = ( V_p i_p )_ V_g = 1 ( i_p V_p )_ V_g Differentiating i_p with respect to V_p keeping V_g constant: i_p V_p = 41 1.41 (V_p + 7 V_g)^ 1.41 - 1 A/V i_p V_p = 57.81 (V_p + 7 V_g)^ 0.41 A/V Substitute the given operating values V_p = 250 V and V_g = -20 V : V_p + 7 V_g = 250 + 7(-20) = 250 - 140 = 110