Condition for Maximum Efficiency in a DC Shunt Machine:

• Power Loss Balance: In a DC shunt generator or motor, total losses comprise constant iron, mechanical, and shunt field losses ($P_i$ or $P_c$) and variable armature copper losses ($I_a^2 R_a$).
• Maximum Efficiency Condition: Efficiency is maximized when the variable loss equals the constant loss:
  $$I_a^2 R_a = P_i$$
• Solving for Armature Current ($I_a$):
  $$I_a^2 = \frac{P_i}{R_a} \implies I_a = \sqrt{\frac{P_i}{R_a}}$$
  where $P_i$ is constant loss and $R_a$ is armature circuit resistance.