The plate current in a triode can be written as i_p = k ! (V_g + V_p )^ 3/2 . The mutual conductance is proportional to what power of the plate current?

Step-by-step solution

The plate current in a triode is given by: i_p = k (V_g + V_p )^ 3/2 The mutual conductance g_m is defined as the rate of change of plate current with respect to grid voltage at a constant plate voltage: g_m = i_p V_g Differentiating the given expression with respect to V_g : g_m = 3 2 k (V_g + V_p )^ 1/2 From the equation for plate current, we can write: (V_g + V_p )^ 3/2 = i_p k (V_g + V_p )^ 1/2 = ( i_p k )^ 1/3 Substituting this back into the expression for mutual conductance: g_m = 3 2 k ( i_p k )^ 1/3 g_m = 3