# Circuit Theory/Variables and Units

## Electric Charge (Coulombs)

Note:
An electron has a charge of
-1.602×10E-19 C.

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric Charge (symbol q) is measured in SI units called "Coulombs", which are abbreviated with the letter capital C.

We know that q=n*e, where n = number of electrons and e= 1.6*10−19. Hence n=1/e coulombs. A Coulomb is the total charge of 6.24150962915265×1018 electrons, thus a single electron has a charge of −1.602 × 10−19 C.

It is important to understand that this concept of "charge" is associated with static electricity. Charge, as a concept, has a physical boundary that is related to counting a group of electrons. "Flowing" electricity is an entirely different situation. "Charge" and electrons separate. Charge moves at the speed of light while electrons move at the speed of 1 meter/hour. Thus in most circuit analysis, "charge" is an abstract concept unrelated to energy or an electron and more related to the flow of information.

Electric charge is the subject of many fundamental laws, such as Coulomb's Law and Gauss' Law (static electricity) but is not used much in circuit theory.

## Voltage (Volts)

Voltage is a measure of the work required to move a charge from one point to another in a electric field. Thus the unit "volt" is defined as a Joules (J) per Coulomb (C).

${\displaystyle V={\frac {W}{q}}}$

W represents work, q represents an amount of charge. Charge is a static electricity concept. The definition of a volt is shared between static and "flowing" electronics.

Voltage is sometimes called "electric potential", because voltage represents the a difference in Electro Motive Force (EMF) that can produce current in a circuit. More voltage means more potential for current. Voltage also can be called "Electric Pressure", although this is far less common.

Voltage is not measured in absolutes but in relative terms. The English language tradition obscures this. For example we say "What is the distance to New York?" Clearly implied is the relative distance from where we are standing to New York. But if we say "What is the voltage at ______?" What is the starting point?

Voltage is defined between two points. Voltage is relative to where 0 is defined. We say "The voltage from point A to B is 5 volts." It is important to understand EMF and voltage are two different things.

When the question is asked "What is the voltage at ______?", look for the ground symbol on a circuit diagram. Measure voltage from ground to _____. If the question is asked "What is the voltage from A to B?" then put the red probe on A and the black probe on B (not ground).

The absolute is referred to as "EMF" or Electro Motive Force. The difference between the two EMF's is a voltage.

## Current (Amperes)

Current is a measurement of the flow of electricity. Current is measured in units called Amperes (or "Amps"). An ampere is "charge volume velocity" in the same way water current could be measured in "cubic feet of water per second." But current is a base SI unit, a fundamental dimension of reality like space, time and mass. A coulomb or charge is not. A coulomb is actually defined in terms of the ampere. "Charge or Coulomb" is a derived SI Unit. The coulomb is a fictitious entity left over from the one fluid /two fluid philosophies of the 18th century.

This course is about flowing electrical energy that is found in all modern electronics. Charge volume velocity (defined by current) is a useful concept, but understand it has no practical use in engineering. Do not think of current as a bundle electrons carrying energy through a wire. Special relativity and quantum mechanics concepts are necessary to understand how electrons move at 1 meter/hour through copper, yet electromagnetic energy moves at near the speed of light.

Charge is similar to the rest mass concept of relativity and generates the U(1) symmetry of electromagnetism

Amperes are abbreviated with an "A" (upper-case A), and the variable most often associated with current is the letter "i" (lower-case I). In terms of coulombs, an ampere is:

${\displaystyle i={\frac {dq}{dt}}}$
For the rest of this book, the lower-case J ( j ) will be used to denote an imaginary number, and the lower-case I ( i ) will be used to denote current.

Because of the widespread use of complex numbers in Electrical Engineering, it is common for electrical engineering texts to use the letter "j" (lower-case J) as the imaginary number, instead of the "i" (lower-case I) commonly used in math texts. This wikibook will adopt the "j" as the imaginary number, to avoid confusion.

## Energy and Power

Electrical theory is about energy storage and the flow of energy in circuits. Energy is chopped up arbitrarily into something that doesn't exist but can be counted called a coulomb. Energy per coulomb is voltage. The velocity of a coulomb is current. Multiplied together, the units are energy velocity or power ... and the unreal "coulomb" disappears.

### Energy

Energy is measured most commonly in Joules, which are abbreviated with a "J" (upper-case J). The variable most commonly used with energy is "w" (lower-case W). The energy symbol is w which stands for work.

From a thermodynamics point of view, all energy consumed by a circuit is work ... all the heat is turned into work. Practically speaking, this can not be true. If it were true, computers would never consume any energy and never heat up.

The reason that all the energy going into a circuit and leaving a circuit is considered "work" is because from a thermodynamic point of view, electrical energy is ideal. All of it can be used. Ideally all of it can be turned into work. Most introduction to thermodynamics courses assume that electrical energy is completely organized (and has entropy of 0).

### Power

A corollary to the concept of energy being work, is that all the energy/power of a circuit (ideally) can be accounted for. The sum of all the power entering and leaving a circuit should add up to zero. No energy should be accumulated (theoretically). Of course capacitors will charge up and may hold onto their energy when the circuit is turned off. Inductors will create a magnetic field containing energy that will instantly disappear back into the source through the switch that turns the circuit off.

This course uses what is called the "passive" sign convention for power. Energy put into a circuit by a power supply is negative, energy leaving a circuit is positive.

Power (the flow of energy) computations are an important part of this course. The symbol for power is w (for work) and the units are Watts or W.