conductor in use for transmission today is aluminum conductor steel reinforced (ACSR). Also seeing much use is all-aluminum-alloy conductor (AAAC). Aluminum is used because it has about half the weight and lower cost of a comparable resistance copper cable. It does, however, require a larger diameter than copper because of lower specific conductivity. Copper was more popular in the past and is still in use, especially at lower voltages and for grounding. While larger conductors lose less energy because of their lower electrical resistance, they cost more than smaller conductors. An optimization rule called Kelvin's Law states that the optimum size of conductor for a line is found when the cost of the energy wasted in a smaller conductor is equal to the annual interest paid on that additional cost of the line construction for a larger conductor. The optimization problem is made more complex by additional factors such as varying annual load, varying cost of installation, and the discrete sizes of cable that are commonly made. Since a conductor is a flexible object with uniform weight per unit length, the shape of a conductor hanging between two towers approximates that of a catenary. The sag of the conductor (vertical distance between the highest and lowest point of the curve) varies depending on the temperature and additional load such as ice cover. A minimum overhead clearance must be maintained for safety. Since the length of the conductor increases with increasing heat produced by the current through it, it is sometimes possible to increase the power handling capacity (uprate) by changing the conductors for a type with a lower coefficient of thermal expansion or a higher allowable operating temperature. Two such conductors that offer reduced thermal sag are known as composite core conductors (ACCR and ACCC conductor). In lieu of steel core strands that are often used to increase overall conductor strength, the ACCC conductor uses a carbon and glass fiber core that offers a coefficient of thermal expansion about 1/10 of that of steel. While the composite core is nonconductive, it is substantially lighter and stronger than steel, which allows the incorporation of 28% more aluminum (using compact trapezoidal-shaped strands) without any diameter or weight penalty. The added aluminum content helps reduce line losses by 25 to 40% compared to other conductors of the same diameter and weight, depending upon electric current. The carbon core conductor's reduced thermal sag allows