Direct Currents Circuits

Direct Current Circuits

These lectures follow the traditional review of direct current circuits, with emphasis on two terminal networks and equivalent circuits. The idea is to bring you up to speed for what is to come. The course will get less quantitative as we go along. In fact, you will probably find the course gets easier as we go.

1.1 Basic Concepts

Direct current (DC) circuit analysis deals with constant currents and voltages, while alternating current (AC) circuit analysis deals with time-varying voltage and current signals whose time average values are zero. Circuits with time-average values of non-zero are also important and will be mentioned briefly in the section on filters. The DC circuit components considered in this course are the constant voltage source, constant current source, and resistor. Electronics also deals with charge Q, electric E and magnetic B fields, as well as, potential V . We will not be concerned with a detailed description of these quantities but will use approximation methods when dealing with them. Hence electronics can be considered as a more practical approach to these subjects.

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1.1.1 Current

The fundamental quantity in electronics is charge and at its basic level is due to the charge properties of the fundamental particles of matter. For all intensive purposes it is the electron (or lack of electrons) that matter. The role of the proton charge is negligible.

The aggregate motion of charges is called current I

I =dq/dt

where dq is the amount of positive charge crossing a specified surface in a time dt. Be aware that the charges in motion are actually negative electrons. Thus the electrons move in the opposite direction to the current flow.

The SI unit for current is the ampere (A). For most electronic circuits the ampere is a

rather large unit so the mA unit is more common.

1.1.2 Potential Difference

It is often more convenient to consider the electrostatic potential V rather than electric

field E as the motivating influence for the flow of electric charge. The generalized vector

properties of E are usually unimportant. The change in potential dV across a distance d_r in an electric field is

dV = −E · d_r.

A positive charge will move from a higher to a lower potential. The potential is also

referred to as the potential difference or, incorrectly, as just voltage:

V = V21 = V2 − V1 = _ V2V1 dV.

Remember that current flowing in a conductor is due to a potential difference between

its ends. Electrons move from a point of less positive potential to more positive potential

and the current flows in the opposite direction.

The SI unit of potential difference is the volt (V).

1.1.3 Resistance and Ohm’s Law

For most materials V ∝ I; V = RI,  where V = V2−V1 is the voltage across the object, I is the current through the object, and R is a proportionality constant called the resistance of the object. Resistance is a function of the material and shape of the object, and has SI units of ohms (Ω). It is more common to find units of kΩ and MΩ. The inverse of resistivity is conductivity.

Resistor tolerances can be as bad as ±20% for general-purpose resistors to ±0.1%

for ultra-precision resistors. Only wire-wound resistors are capable of ultraprecision

applications. The concept of current through and potential across are key to the understanding of and sounding intelligent about electronics.

Now comes the most  useful visual tool of this course.

1.2 The Schematic Diagram

The schematic diagram consists of idealized circuit elements each of which represents some property of the actual circuit.  shows some common circuit elements encountered

in DC circuits. A two-terminal network is a circuit that has only two points of interest, say

A and B.

1.2.1 Electromotive Force (EMF)

Charge can flow in a material under the influence of an external electric field. Eventually

the internal field due to the repositioned charge cancels the external electric field resulting in zero current flow. To maintain a potential drop (and flow of charge) requires an external energy source, ie. EMF (battery, power supply, signal generator, etc.). We will deal with two types of EMFs:

The ideal voltage source is able to maintain a constant voltage regardless of the current

it must put out (I →∞ is possible).

The ideal current source is able to maintain a constant current regardless of the voltage

needed (V →∞ is possible).

Because a battery cannot produce an infinite amount of current, a model for the behavior of a battery is to put an internal resistance in series with an ideal voltage source (zero resistance). Real-life EMFs can always be approximated with ideal EMFs and appropriate combinations of other circuit elements.

1.2.2 Ground

A voltage must always be measured relative to some reference point. It is proper to speak of the voltage across an electrical component but we often speak of voltage at a point. It is then assumed that the reference voltage point is ground. Under strict definition, ground is the body of the earth. It is an infinite electrical sink.

It can accept or supply any reasonable amount of charge without changing its electrical

characteristics. It is common, but not always necessary, to connect some part of the circuit to earth or ground, which is taken, for convenience and by convention, to be at zero volts. Frequently, a common (or reference) connection of the metal chassis of the instrument suffices. Sometimes there is a common reference voltage that is not at 0 V. Figure 1.2 show some common ways of depicting grounds on a circuit diagram.

When neither a ground nor any other voltage reference is shown explicitly on a schematic diagram, it is useful for purposes of discussion to adopt the convention that the bottom line on a circuit is at zero potential.