Lesson 2 Charge，Current and Voltage

One of the most fundamental concepts in electric circuit analysis is charge conservation. We know from basic physics that there are two types of charge:positive（corresponding to a proton），and negative（corresponding to an electron）.For the most part，this text is concerned with circuits in which only electron flow is relevant.There are many devices（such as batteries，diodes，and transistors）in which positive charge motion is important to understanding internal operation，but external to the device we typically concentrate on the electrons which flow through the connecting wires.Although we continuously transfer charges between different parts of a circuit，we do nothing to change the total amount of charge. In other words，we neither create nor destroy electrons（or protons）when running electric circuits.Charge in motion represents a current.

In the SI system，the fundamental unit of charge is the coulomb（C）.It is defined in terms of the ampere by counting the total charge that passes through an arbitrary cross section of a wire during an interval of one second;one coulomb is measured each second for a wire carrying a current of 1 ampere.In this system of units，a single electron has a charge of?1.602×10-19 C and a single proton has a charge of+1.602×10-19 C.

A quantity of charge that does not change with time is typically represented by Q.The instantaneous amount of charge（which may or may not be time-invariant）is commonly represented by q（t），or simply q.This convention is used throughout the remainder of the text:capital letters are reserved for constant（time-invariant）quantities，whereas lowercase letters represent the more general case.Thus，a constant charge may be represented by either Q or q，but an amount of charge that changes over time must be represented by the lowercase letter q.

The idea of"transfer of charge"or"charge in motion"is of vital importance to us in studying electric circuits because，in moving a charge from place to place，we may also transfer energy from one point to another.The familiar cross-country power-transmission line is a practical example of a device that transfers energy.Of equal importance is the possibility of varying the rate at which the charge is transferred in order to communicate or transfer information. This process is the basis of communication systems such as radio，television，and telemetry.

The current present in a discrete path，such as a metallic wire，has both a numerical value and a direction associated with it;it is a measure of the rate at which charge is moving past a given reference point in a specified direction.

Once we have specified a reference direction，we may then let q（t）be the total charge that has passed the reference point since an arbitrary time t=0，moving in the defined direction.A contribution to this total charge will be negative if negative charge is moving in the reference direction，or if positive charge is moving in the opposite direction.

We define the current at a specific point and flowing in a specified direction as the instantaneous ous rate at which net positive charge is moving past that point in the specified direction.This，un-fortunately，is the historical definition，which came into popular use before it was appreciated that current in wires is actually due to negative，not positive，charge motion.Current is symbolized by I or i，and so

The unit of current is ampere（A），named after A.M.Ampere，a French physicist.It is commonly abbreviated as an"amp"，although this is unofficial and somewhat informal.

Using Eq.（2.1），we compute the instantaneous current.The use of the lowercase letter"i"is again to be associated with an instantaneous value;an uppercase"I"would denote a constant（i.e.，time-invariant）quantity.

The charge transferred between time t0 and t may be expressed as a definite integral:

The total charge transferred over all time is obtained by adding q（t0），the charge transferred up to the time t0，to the preceding expression:

There are several different types of current.A current that is constant in time is termed a direct current，or simply DC.We will find many practical examples of currents that vary sinusoidally with time;currents of this form are present in normal household circuits.Such a current is often referred to as alternating current，or AC. Exponential currents and damped sinusoidal currents will also be encountered later.

We establish a graphical symbol for current by placing an arrow next to the conductor.Thus，in Fig.2.1 the direction of the arrow and the value"3A"indicate either that a net positive charge of 3C is moving to the right or that a net negative charge of-3C is moving to the left each second.In Fig. 2.2 there are again two possibilities:either-3A is flowing to the left or+3A is flowing to the right. All four statements and both figures represent currents that are equivalent in their electrical effects，and we say that they are equal.A nonelectrical analogy that may be easier to visualize is to think in terms of a personal savings account:e.g.，a deposit can be viewed as either a negative cash flow out of your account or a positive flow into your account.

It is convenient to think of current as the motion of positive charge，even though it is known that current flow in metallic conductors results from electron motion.In ionized gases，in electrolytic solutions，and in some semiconductor materials，positively charged elements in motion constitute part or all of the current.Thus，any definition of current can agree with the physical nature of conduction only part of the time.The definition and symbolism we have adopted are standard.

It is essential that we realize that the current arrow does not indicate the"actual"direction of current flow but is simply part of a convention that allows us to talk about"the current in the wire"in an unambiguous manner.The arrow is a fundamental part of the definition of a current！Thus，to talk about the value of a current il（t）without specifying the arrow is to discuss an undefined entity. For example，Fig.2.3 and Fig.2.4 are meaningless representations of il（t），whereas Fig.2.5 is the proper definitive symbology.

We must now begin to refer to a circuit element，something best defined in general terms to begin with.Such electrical devices as fuses，light bulbs，resistors，batteries，capacitors，generators，and spark coils can be represented by combinations of simple circuit elements.We begin by showing a very general circuit element as a shapeless object possessing two terminals at which connections to other elements may be made.

There are two paths by which current may enter or leave the element.In subsequent discussions we will define particular circuit elements by describing the electrical characteristics that may be observed at their terminals.

In Fig.2.6，let us suppose that a DC current is sent into terminal A，through the general element，and back out of terminal B.Let us also assume that pushing charge through the element requires an expenditure of energy.We then say that an electrical voltage（or a potential difference）exists between the two terminals，or that there is a voltage"across"the element.Thus，the voltage across a terminal pair is a measure of the work required to move charge through the element. The unit of voltage is volt，and 1 volt is the same as 1 J/C.Voltage is represented by V or v.

A voltage can exist between a pair of electrical terminals whether a current is flowing or not. An automobile battery，for example，has a voltage of 12 V across its terminals even if nothing whatsoever is connected to the terminals.

According to the principle of conservation of energy，the energy that is expended in forcing charge through the element must appear somewhere else. When we later meet specific circuit elements，we will note whether that energy is stored in some form that is readily available as electric energy or whether it changes irreversibly into heat，acoustic energy，or some other nonelectrical form.

We must now establish a convention by which we can distinguish between energy supplied to an element，and energy that is supplied by the element itself.We do this by our choice of sign for the voltage of terminal A with respect to terminal B.If a positive current is entering terminal A of the element and an external source must expend energy to establish this current，then terminal A is positive with respect to terminal B.Alternatively，we may say that terminal B is negative with respect to terminal A.

The sense of the voltage is indicated by a plus-minus pair of algebraic signs.For example，the placement of the"+"sign at terminal A indicates that terminal A is v volts positive with respect to terminal B.If we later find that v happens to have a numerical value of-5V，then we may say either that A is-5V positive with respect to B or that B is 5V positive with respect to A.

Just as we noted in our definition of current，it is essential to realize that the plus-minus pair of algebraic signs does not indicate the"actual"polarity of the voltage but is simply part of a convention that enables us to talk unambiguously about "the voltage across the terminal pair". Note: The definition of any voltage must include a plus-minus sign pair！