An understanding of circuits must be built on a basic knowledge of electrical physics. One must be familiar with electrical quantities, such as charge, current, and voltage, which are used in describing the operation of circuits. It is expected that to most readers, the material of this section will not be entirely new. Nonetheless, it will serve as review, and will also familiarize the reader with our definitions, notation, and point of view.
The branch of physics known as electricity seeks to describe electrical phenomena in terms of mathematical equations. The quantities in these equations must describe specifically electrical conditions, and hence are called electrical quantities. As with other physical quantities, electrical quantities must be expressed in a consistent system of units. The system of units to be used throughout this book is known as the International System (or System Internationale), and the units are referred to as SI units. A summary of these units is given in Table 1.1.
The three most fundamental electrical quantities are charge, current, and voltage. We shall now review the meaning of these terms in detail.

Charge
Each kind of atomic particle carries a certain amount of charge. In the international system of units, charge is measured in coulombs (C). Experimentally it is found that the neutron has a charge of zero. The proton has a charge of +1.6 x 1019 coulombs; this amount of charge is given the symbol q. The electron has a charge which is exactly equal to that of the proton but opposite in sign; that is, the charge of an electron is 1.6 x 1019 C, or – q. It is also found experimentally that the charge q is the smallest unit of charge that exists in nature. Larger charges occur when many charged particles are collected together. However, the coulomb is a large unit. Charges as large as 1 C may occur in electric power systems, but they almost never are found in electronics.
Example
Throughout most of its volume, an impure silicon crystal contains equal densities of electrons (each with charge – q) and positive ions (each with charge +q). However, there is a small region, with dimensions 5 x 104 em by 1 mm by 1 mm, where only the ions are present. The density of ions everywhere in the crystal is 1022/m3. Find the total charge of the crystal.
Solution
In the region where both ions and free electrons are present, their opposite charges cancel, and the charge density is O. Hence the total charge of the crystal arises from the region containing ions only. The charge density here is given by the number of ions per unit volume times the charge of each ion; the latter quantity is +q, or 1.6 x 1019 C. Thus
p = (1022) . (1.6 x 1019) C/m3 = 1.6 x 103 C/m3
The total charge Q is equal to the charge density (charge per unit volume) p times the volume of the charged region. In computing the latter we must convert the given dimensions to SI units:
V = (5 X 106 m) . (103 m) . (103 m) = 5 X 1012 m3
Table 1.1 The SI units
For example, 1 nanosecond (nsec) is 109 second; 1 kilo volt (kV) is 1000 V. These units are often more convenient than the basic SI units; for instance, it is handier to write “1.6 IJ.A” than “0.0000016 A.” However, it should be remembered that almost all equations in this book are true statements only when all quantities are expressed in the basic SI units. Numerical errors can occur if the prefixed units are carelessly used instead.
Current
A flow of electrical charge from one region to another is called a current. Currents have not only magnitude, but also direction. To indicate its direction, a current is described by a number with a sign. At the top the current in the wire has been given the name II’ We indicate this by writing “II” next to the wire; in addition, we draw a small arrow along the wire. The arrow is important. It means that the current in the direction of the arrow has the value I i The direction of the arrow is called the reference direction of II’ The choice of which direction is the reference direction is arbitrary. This choice is simply part of the process of naming the current.
By definition, a positive current exists when positive charges move in the reference direction, as illustrated by Case. In Case (a) the numerical value of II will be positive. However, if positive charges move opposite to the reference direction, the current has a negative value. The current could also arise from motion of negative charges, as in Cases (b) and (d) When negative charges are moving the sign of the current is reversed from what it would be if positive charges were moving. Suppose a quantity of charge dQ moves past some point in the reference direction in time dt. Then the value of the current is dQ/dt. If a charge dQ moves opposite to the reference direction in time dt, the current is – dQ/dt.
The reference direction of current I, is chosen to be from left to right, as indicated by the arrow. In cases (a) and (b) the numerical value of I, is positive. In cases (c) and (d) the numerical value of I, is negative.
The SI unit of current is the ampere, 1 ampere (A) representing a current of 1 coulomb per second.
Example
(a) the current I, has the reference direction indicated. The current arises from the motion of 1013 electrons per second, as shown. What is the value of Ix?
(b) shows exactly the same charges moving in the same way. However, we have chosen to define a new current Iy whose reference direction is opposite from that chosen for IX’ What is the value of Iy?
Solution
(a) In this case we have negative charges moving in the reference direction. Hence the numerical value of the current is +dQ/dt, where dQ, the charge transferred in time dt, is a negative number. Hence
I, = (1.6 x 10 19)(1013) = 1.6 f,IA
(b) In this case the charges are moving opposite to the reference direction. Hence the current in the reference direction is – dQ/dt, where dQ is a negative number. Thus
Iy = – (1.6 x 1019)(1013) = + 1.6 f,IA
Note: In everyday speech, one often hears expressions like “the current is in the direction from A to B.” What is meant is that the sign of the current is the same as if positive charges were moving from A to B.