The correct answer is D) speed control. The variable resistance placed in the rotor circuit of a wound-rotor induction motor is used to control the speed of the motor. By adjusting the resistance in the rotor circuit, the rotor current and, consequently, the torque developed by the motor can be varied, allowing for speed control. This method is commonly used in applications where a wide range of speed control is required, such as in cranes, hoists, and elevators. The other options are incorrect because they do not accurately describe the purpose of the variable resistance in the rotor circuit. Frequency control (A) is typically achieved through other means, such as using a variable-frequency drive. Voltage control (B) is not the primary purpose of the variable resistance. Torque control (C) is a secondary effect, as the primary purpose is speed control.