By substituting equations 3. and 4. (torque and speed, section 2.1) into equation 2. (power, section 1.3 ), we see that the power curves for a D.C. motor with respect to both speed and torque are quadratics, as shown in equations 5. and 6. From these equations, we again find that maximum output power occurs at = ½, and = ½ repectively.