advantages of alternating current over direct current in using transformers to raise and lower voltages to allow much longer transmission distances, direct current was replaced over the next few decades by alternating current in power delivery. In the mid-1950s, high-voltage direct current transmission was developed, and is now an option instead of long-distance high voltage alternating current systems. For long distance undersea cables (e.g. between countries, such as NorNed), this DC option is the only technically feasible option. For applications requiring direct current, such as third rail power systems, alternating current is distributed to a substation, which utilizes a rectifier to convert the power to direct current. Various definitions The term DC is used to refer to power systems that use only one electrical polarity of voltage or current, and to refer to the constant, zero-frequency, or slowly varying local mean value of a voltage or current. For example, the voltage across a DC voltage source is constant as is the current through a DC current source. The DC solution of an electric circuit is the solution where all voltages and currents are constant. It can be shown that any stationary voltage or current waveform can be decomposed into a sum of a DC component and a zero-mean time-varying component; the DC component is defined to be the expected value, or the average value of the voltage or current over all time. Although DC stands for "direct current", DC often refers to "constant polarity". Under this definition, DC voltages can vary in time, as seen in the raw output of a rectifier or the fluctuating voice signal on a telephone line. Some forms of DC (such as that produced by a voltage regulator) have almost no variations in voltage, but may still have variations in output power and current. Circuits A direct current circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors. In this case, the circuit voltages and currents are independent of time. A particular circuit voltage or current does not depend on the past value of any circuit voltage or current. This implies that the system of equations that represent a DC circuit do not involve integrals or derivatives with respect to time. If a capacitor or inductor is added to a DC circuit, the resulting circuit is not, strictly speaking, a DC circuit. However, most such circuits