Answer
For a given force, we can create more torque by using a thicker handle. Similarly, we can create the same torque with a smaller applied force if we use a thicker handle.
Work Step by Step
The torque is proportional to the distance from the point where the force is applied to the the axis of rotation. If the handle is the thicker, then the distance between the applied force and the axis of rotation is greater. Therefore, for a given force, we can create more torque by using a thicker handle. Similarly, we can create the same torque with a smaller applied force if we use a thicker handle.