# Brushing up on dc circuit fundamentals

## Before you get out of bed each day, an electronic clock radio awakens you so that you can get ready for your commute to the plant. Perhaps your car or truck has electronic fuel injection — not to mention a main computer that can be serviced only at the dealership. At the plant, you encounter electronic circuits, equipment, and systems — some of which you probably take for granted.

Before you get out of bed each day, an electronic clock radio awakens you so that you can get ready for your commute to the plant. Perhaps your car or truck has electronic fuel injection — not to mention a main computer that can be serviced only at the dealership.

At the plant, you encounter electronic circuits, equipment, and systems — some of which you probably take for granted. The presence of electronic items seems to be universal, from the ubiquitous computer to the time clock, to the controls on the equipment in manufacturing areas, to the scales on the loading dock.

If you maintain electronic equipment and systems in your job, you understand the theories and laws that govern the field. However, whether you are new to electronics or a seasoned pro, a refresher course in the fundamentals can be helpful. These fundamentals begin with how electricity behaves in dc circuits.

## Characteristics of electricity

Opposite electrical charges attract, while like electrical charges repel. A negative charge is a surplus of electrons, while a positive charge is a deficiency of electrons. When there is a surplus of electrons, there is potential for these electrons to equalize, creating the tendency for electrons to try to get to a positively charged region to satisfy the electron deficiency. This abstract explanation describes a battery or other source of dc electrical energy.

Getting the abundant electrons from the negative region, or battery terminal, to the positive region requires a path along which these electrons can flow. Obviously, an electrical conductor allows this to happen, while an insulator attempts to prevent this from happening. Most metals conduct electrical current, but copper is the best practical conductor of electricity because of its number of valence electrons and because it is a relatively economical material.

Valence electrons are often referred to as ‘loose’ electrons. Actually, they are loosely held in their orbits around the nucleus of the atom. When a conductor is placed between two charged objects, these loosely held valence electrons are pushed away by the negatively charged object and are pulled into the positively charged object. The resulting electron flow is called current.

If there is a balance of electrons between two objects, then there is neither a surplus nor deficiency of electrons, and therefore no negative or positive charges. However, to get current to flow, there must be an unbalance, which is called a difference in potential, or voltage. It is voltage that provides the electrical ‘push’ which causes current to flow through a conductor.

To complete this theoretical circuit, there must be a conductor connected between the negative and positive terminals to the voltage source, or battery. However, connecting a wire across a battery would not be very practical. The resulting heavy current would heat the wire. It would not take very long for the battery to be dead because the electrons would have equalized across the battery. The circuit needs something to slow down — or resist — the flow of current. This is impedance to the flow of electrons is called resistance.

Even the best electrical conductors have some resistance. On a practical level, don’t depend on that extremely low resistance to limit current. How useful would this electrical theory be if all we did were to connect wires to batteries? Connecting some type of load between the positive and negative terminals limits the current flow, allows the battery to last longer, and actually can be useful. For example, a simple flashlight connects batteries to a lamp when the switch is closed. Completing this circuit allows current to flow through the bulb, which provides some resistance. The current flowing through the bulb produces light.

Whether lighting a bulb, heating a substance, or spinning a motor, whenever current flows, work is done.

## Ohm’s Law

Water can be used to help describe the behavior of an electrical circuit. Just as the flow of water is known as current, the flow of electrons is known as current too. Voltage is electrical pressure. A pump is a source of water pressure, while a battery is a source of electrical pressure. A valve or other obstruction presents impedance to the flow of water. A resistor, lamp, or other electrical resistance presents impedance to electrical flow.

These electrical theories must be quantified to be useful in the real world. The unit of voltage is the volt (V); the unit of current is the ampere (A); and the unit of resistance is the Ohm. The relationship among these electrical parameters is Ohm’s Law (See “Ohm’s Law pyramid”). This simple relationship establishes the foundation upon which electrical and electronic concepts are built.

Within an electrical circuit, 1 V causes 1 A to flow through 1 Ohm. In the Ohm’s Law formulas, ‘V’ represents voltage, ‘R’ represents resistance, and ‘I’ represents current. To find the current flowing through a resistance, divide the voltage across that resistance by the value of the resistance:

*I=V/R*

If you want to know the resistance, and you know the current flowing through it and the voltage drop across it, divide the voltage by the current:

*R=V/I*

If you know the resistance and the amount of current flowing through it, multiply the current and the resistance to get the voltage across the resistance:

*V = I*R*

For example, consider a circuit with a 10-V battery connected to a 1000-Ohm resistor (Fig. 1). The current flowing through the resistor, as well as the rest of the circuit, is 0.01 A.

## Kirchhoff’s Laws

Kirchhoff’s circuit rules, named after Gustav Robert Kirchhoff, are two statements about multi-loop electric circuits that convey the laws of conservation of electric charge and energy, and that are used to determine the value of the electric current in each branch of the circuit.

The first rule is the junction theorem, which states that the sum of the currents into a specific junction in the circuit equals the sum of the currents out of the same junction. Electric charge is conserved. In other words, regardless of the number of paths into and out of a single point, all the current leaving that point must equal the current arriving at that point (Fig. 2).

Kirchhoff’s second rule is the loop equation, which states that around each loop in an electric circuit, the supplied voltage is equal to the sum of the potential drops, or voltages across each of the resistances, in the same loop. All the energy imparted by the energy sources to the charged particles that carry the current is just equivalent to that lost by the charge carriers in useful work and heat dissipation around each loop of the circuit. In other words, the voltage drops around any closed loop must equal the applied voltages (Fig. 3).

Based on Kirchhoff’s Laws, equations can be written to determine each of the currents algebraically. With appropriate modifications, Kirchhoff’s circuit rules are also applicable to complex ac and magnetic circuits.

Sometimes circuits contain several resistance elements, more than one current path, or both. If resistances are connected in series, their resistance values are added to obtain the total circuit resistance.

*R* _{T} = *R* _{1} + *R* _{2} + *R* _{3} + *…R* _{n}

*Where R _{T} is the value of the total resistance and R _{n} is the value of the nth resistance. All resistances values are in Ohms.*

If resistances are connected in parallel, their effective resistance is the inverse of the sum of their inverse resistances. If two resistors are connected in parallel:

If multiple resistors are connected in parallel:

To simplify resistance networks, replace several resistances with one equivalent resistance. Start by adding the series resistances. Then collapse parallel branches into one equivalent resistance. Add this value to the previously calculated series resistances. Continue this process until only one equivalent resistance remains.

Although electrical conductors contain some resistance, when compared to resistors used in electrical and electronic circuits, the resistance value of conductors is virtually negligible. Even batteries, which are voltage sources, have some internal resistance. For the purpose of understanding fundamental theories, these minute resistances will be ignored. However, to under-stand how components behave in electronic circuits, it is important to know the relationships among their values (See “Determining the value of resistors”).

Regardless of your level of experience, a reminder of the fundamentals can help you maintain electronic equipment and systems.

## Ohm’s Law pyramid

**Georg Simon Ohm** is credited with quantifying the relationship among the parameters in an electrical circuit. Unfortunately, when Ohm published his finding in 1827, his colleagues dismissed his ideas. However, the principles he discovered have survived to become the basis of electrical and electronics theory, which is why the relationship among voltage, current, and resistance bears his name. The pyramid is a classic way to illustrate these relationships and how to calculate them.

**To use the pyramid** , place your finger over the value you wish to find. If you wish to find V, multiply I by R. If you wish to find I, divide V by R.

## Ohm’s Law pyramid

**Georg Simon Ohm** is credited with quantifying the relationship among the parameters in an electrical circuit. Unfortunately, when Ohm published his finding in 1827, his colleagues dismissed his ideas. However, the principles he discovered have survived to become the basis of electrical and electronics theory, which is why the relationship among voltage, current, and resistance bears his name. The pyramid is a classic way to illustrate these relationships and how to calculate them.

**To use the pyramid** , place your finger over the value you wish to find. If you wish to find V, multiply I by R. If you wish to find I, divide V by R.

## Ohm’s Law pyramid

**Georg Simon Ohm** is credited with quantifying the relationship among the parameters in an electrical circuit. Unfortunately, when Ohm published his finding in 1827, his colleagues dismissed his ideas. However, the principles he discovered have survived to become the basis of electrical and electronics theory, which is why the relationship among voltage, current, and resistance bears his name. The pyramid is a classic way to illustrate these relationships and how to calculate them.

**To use the pyramid** , place your finger over the value you wish to find. If you wish to find V, multiply I by R. If you wish to find I, divide V by R.

## Ohm’s Law pyramid

**Georg Simon Ohm** is credited with quantifying the relationship among the parameters in an electrical circuit. Unfortunately, when Ohm published his finding in 1827, his colleagues dismissed his ideas. However, the principles he discovered have survived to become the basis of electrical and electronics theory, which is why the relationship among voltage, current, and resistance bears his name. The pyramid is a classic way to illustrate these relationships and how to calculate them.

**To use the pyramid** , place your finger over the value you wish to find. If you wish to find V, multiply I by R. If you wish to find I, divide V by R.

## Ohm’s Law pyramid

**Georg Simon Ohm** is credited with quantifying the relationship among the parameters in an electrical circuit. Unfortunately, when Ohm published his finding in 1827, his colleagues dismissed his ideas. However, the principles he discovered have survived to become the basis of electrical and electronics theory, which is why the relationship among voltage, current, and resistance bears his name. The pyramid is a classic way to illustrate these relationships and how to calculate them.

**To use the pyramid** , place your finger over the value you wish to find. If you wish to find V, multiply I by R. If you wish to find I, divide V by R.

## Determining the value of resistors

The color bands around typical resistors represent their resistance values in Ohms. The first two bands are numerical values. The third band is a power-of-ten multiplier for the value given by the first two bands. The fourth band is the tolerance band. Gold is 5%, silver is 10%, and the absence of a fourth band indicates 20% tolerance. For example, a resistor marked with red-red-orange-gold bands has a value of 22,000 (22 K) Ohms,

Resistor color code

Color |
Significant figures (bands 1 and 2) |
Multiplier (third band) |
Tolerance (fourth band) |

Black | 0 | 1 | — |

Brown | 1 | 10 | |

Red | 2 | 100 | |

Orange | 3 | 1000 | |

Yellow | 4 | 10,000 | |

Green | 5 | 100,000 | — |

Blue | 6 | 1,000,000 | — |

Violet | 7 | 10,000,000 | — |

Gray | 8 | 100,000,000 | — |

White | 9 | — | — |

Gold | — | 0.1 | |

Silver | — | 0.01 | |

No color | — | — |

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