Last month, we introduced the fundamental quantities of voltage, current, and power, and described the basic elements of electrical circuits. In this column, we will put these basic elements together into the simplest electrical system, the direct current (dc) circuit.

## DC Circuits

In dc circuits, the polarity of the voltage source does not change over time. Common dc sources include batteries, photocells, fuel cells, and rectifiers, which convert ac voltage into dc voltage. When a dc source is connected in a closed electrical circuit, current will flow in a direction determined by the polarity of the source. By convention, we show dc current flow as originating at the positive terminal of the source, travelling through the circuit and returning to the negative terminal.

A hydraulic analog helps to demonstrate the relationships between the basic quantities in a simple dc circuit.

In Figure 1, when the switch is closed, the potential difference of the source pushes current through the resistance of the load. The voltage across the load is equal to the source voltage if the switch and the wires have negligible resistance.

Figure 2 shows the hydraulic equivalent. When the valve is opened, the pressure developed by the pump forces fluid flow through the coil, and the pressure drop across the coil equals the pump ?P if the head loss in the valve and the piping is negligible.

While useful for understanding the basics, the hydraulic analogy has its limits. For electric current to flow, there must always be a closed-circuit path back to the source. Unlike a storage tank in an open hydraulic circuit, an electric source like a battery cannot be "pumped down." If the return circuit path is opened, the current will cease to flow.

The analogy also fails mathematically, since the equations for the basic quantities in the two circuits are not the same. In the electrical circuit, current flow is linear with voltage (I = V ? R), whereas the flow in the hydraulic circuit is proportional to the square root of the pressure difference (Q = CvP, where C is a constant).

## Voltage Drop

By making an analogy to pressure differentials in the hydraulic circuit, we can illustrate a fundamental concept of circuit analysis that applies to both dc and ac circuits:The sum of the voltage differences across each of the elements in a completed circuit must equal the source voltage.

In an ideal (loss-less) hydraulic circuit consisting of a pump and a coil, the full pressure differential developed by the pump must appear across the coil. In an ideal electrical circuit, the full voltage developed by the source appears across the load. Just as a real-world hydraulic circuit has head loss in the piping, the conductors connecting the components together in real electrical circuits have resistance, which creates voltage drop between the source and the load.

Consider the circuit in Figure 3, in which the 24-V power supply must operate the damper motor, which is located 200 ft from the control panel. If the damper motor draws 1 A and each conductor has 1.6 Ohms of resistance (#18 AWG copper at 8 Ohms/ 1,000 ft), the voltage dropped across the conductors results in 20.8 V at the motor. If the motor cannot deliver the required amount of torque at this voltage, the wire size must be increased to reduce the voltage drop.

Next month we will extend these concepts to alternating current (ac) circuits, and introduce the concepts of frequency, phase, and power factor. A basic understanding of these concepts is essential to working with building power systems and specifying motors and drives for hvacr equipment.ES