In the field of electronics theory, the direct current, or DC circuit is usually the first circuit studied. A DC circuit consists of only a few of the most basic components: a source of electromotive force, a method of connecting components together and providing a path for electron flow, and a device that the electromotive force and electrons act upon. In a simple analysis such as this, this device is anything that resists the flow of electrons and is referred to as a “resistor.”

The function of the battery is to provide a difference of electrical potential between two points. The electrical difference of potential, or electromotive force, is measured in terms of a Volt, named after an Italian physicist that first invented the chemical battery.

When the opposite poles of a battery are connected together by a conducting mechanism, such as a strand of copper wire, electrons will flow from the negative pole of the battery to the positive pole in an attempt to create electrical equilibrium. The rate of flow of the electrons through the conductor is termed current and is represented by the symbol “I”.

According to Ohm’s law, the rate of current flow “I” is proportional to the amount of electro-motive force “E”, divided by the total resistance connected across its terminals. This is the most basic explanation of the behavior of electron flow, expressed in formula notation as I=E/R. Current flow is measured in Amperes, and is commonly referred to as “Amps.”

The most familiar source of the electromotive force is the battery. Batteries come in different shapes and sizes ranging from the typical dry cell battery used in flashlights, cameras, portable radios, and calculators, to the 12-volt wet cell battery that starts up your car on demand. There are other types of batteries as well, such and the Lithium-ion battery and the Nickel Cadmium battery. These are typically used to provide low voltages in a low current situation.

Resistors are passive devices, meaning that they do not change their characteristics if the electromotive force or the current flow changes. Devices that do change are referred to as reactive devices and exhibit a property referred to as “reactance”. Two such devices are capacitors and inductors and are most useful in alternating current (AC) devices. These devices store energy in electrostatic or electromagnetic fields, respectively.

A typical resistor is constructed from a small bar of carbon with a wire attachment at each end. The behavior of carbon to the flow of electrical current is well known and the amount of resistance can be established by varying the size of the carbon bar. Resistors of this type are designed to dissipate heat and are rated according to the amount of heat they can handle effectively before breaking down.

The amount of resistance seen by a battery can be calculated by adjusting Ohm’s law to solve for by making R the unknown value. In this simple formula, R=E/I.

In a simple series DC circuit, the total resistance is the sum of all resistive components present in the circuit. In other words, if R1= the value of the first resistor and R3= the value of the last resistor, than the total resistance in a three resistor circuit, Rt, equals R1+R2+R3. So, if each resistor equals a resistance value of 5, then Rt=5+5+5, = 15 ohms.

In a circuit where resistors are connected in parallel, or across each other, the total resistance is calculated differently. Since there are several different paths, or legs for current to flow through in a parallel circuit, the total current is divided between each leg according to the amount of resistance present in it. The applied electromotive difference of potential E, remains constant. Total current, or It is the sum of the individual current flow through each leg. It=I1+I2+I3. The total resistance seen at the source of electromotive difference of potential (battery) is the inverse sum of all resistors connected in parallel, or Rt=1/1/r1+1/r2+1/r3

Once the value of R is known, the value of either current can be solved for by adjusting the Ohm’s law formula to one of its two remaining variations. I=E/R, or E=IR for the respective leg.

The resistance to current flow consumes electromotive energy, referred to as power, in the form of heat. Power consumption is calculated by squaring the amount of current flow and multiplying it by the value of resistance present. In other words, P=I2R.

A nice explanation of this relationship can be found at http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepow.html#c1

Resistors can be fixed or variable, depending upon the design of the circuit in which they are applied. Variable resistors are referred to as Potentiometers”, or “Rheostats”. These devices are made adjustable by applying increasing amounts of carbon within container. A tapping point or conductor slides across a given range of resistance determined by its construction.

In a typical application the brightness of a lamp is increased or decreased by turning a knob attached to a potentiometer. It works by either reducing or increasing the current flow through the lamp, thereby altering the lamp’s brightness. Resistors and many other electrical devices are sometimes referred to as the “electrical load” or simply the “load’ on a source of power, such as a battery.