Electronics

An **electronic component** is any basic **discrete device** or physical entity in an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are not to be confused with electrical elements, which are conceptual abstractions representing idealized electronic components.

Electronic components have a number of electrical terminals or leads. These leads connect to other electrical components, often over wire, to create an electronic circuit with a particular function (for example an amplifier, radio receiver, or oscillator). Basic electronic components may be packaged discretely, as arrays or networks of like components, or integrated inside of packages such as semiconductor integrated circuits, hybrid integrated circuits, or thick film devices. The following list of electronic components focuses on the discrete version of these components, treating such packages as components in their own right.

Components can be classified as passive, active, or electromechanic. The strict physics definition treats passive components as ones that cannot supply energy themselves, whereas a battery would be seen as an active component since it truly acts as a source of energy.

However, electronic engineers who perform circuit analysis use a more restrictive definition of passivity. When only concerned with the energy of signals, it is convenient to ignore the so-called DC circuit and pretend that the power supplying components such as transistors or integrated circuits is absent (as if each such component had its own battery built in), though it may in reality be supplied by the DC circuit. Then, the analysis only concerns the AC circuit, an abstraction that ignores DC voltages and currents (and the power associated with them) present in the real-life circuit. This fiction, for instance, lets us view an oscillator as "producing energy" even though in reality the oscillator consumes even more energy from a DC power supply, which we have chosen to ignore. Under that restriction, we define the terms as used in circuit analysis as:

* **Active components** rely on a source of energy (usually from the DC circuit, which we have chosen to ignore) and usually can inject power into a circuit, though this is not part of the definition. Active components include amplifying components such as transistors, triode vacuum tubes (valves), and tunnel diodes.
* **Passive components** can't introduce net energy into the circuit. They also can't rely on a source of power, except for what is available from the (AC) circuit they are connected to. As a consequence they can't amplify (increase the power of a signal), although they may increase a voltage or current (such as is done by a transformer or resonant circuit). Passive components include two-terminal components such as resistors, capacitors, inductors, and transformers.
* **Electromechanical components** can carry out electrical operations by using moving parts or by using electrical connections

Most passive components with more than two terminals can be described in terms of two-port parameters that satisfy the principle of reciprocity—though there are rare exceptions. In contrast, active components (with more than two terminals) generally lack that property.

### Resistors

Main articles: Ohm's law
The behaviour of an ideal resistor is dictated by the relationship specified by Ohm's law:

# V
I
⋅
R
.

{\displaystyle V=I \cdot R.}

Ohm's law states that the voltage (V) across a resistor is proportional to the current (I), where the constant of proportionality is the resistance (R). For example, if a 300 ohm resistor is attached across the terminals of a 12 volt battery, then a current of 12 / 300 = 0.04 amperes flows through that resistor.

Practical resistors also have some inductance and capacitance which affect the relation between voltage and current in alternating current circuits.

The ohm (symbol: Ω) is the SI unit of electrical resistance, named after Georg Simon Ohm. An ohm is equivalent to a volt per ampere. Since resistors are specified and manufactured over a very large range of values, the derived units of milliohm (1 mΩ = 10−3 Ω), kilohm (1 kΩ = 103 Ω), and megohm (1 MΩ = 106 Ω) are also in common usage.

### Capacitors

A capacitor consists of two conductors separated by a non-conductive region. The non-conductive region can either be a vacuum or an electrical insulator material known as a dielectric. Examples of dielectric media are glass, air, paper, plastic, ceramic, and even a semiconductor depletion region chemically identical to the conductors. From Coulomb's law a charge on one conductor will exert a force on the charge carriers within the other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity charge will be induced on the surface of the other conductor. The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field.

An ideal capacitor is characterized by a constant capacitance *C*, in farads in the SI system of units, defined as the ratio of the positive or negative charge *Q* on each conductor to the voltage *V* between them:

# C

Q
V

{\displaystyle C = \frac{Q}{V} }

A capacitance of one farad (F) means that one coulomb of charge on each conductor causes a voltage of one volt across the device. Because the conductors (or plates) are close together, the opposite charges on the conductors attract one another due to their electric fields, allowing the capacitor to store more charge for a given voltage than when the conductors are separated, yielding a larger capacitance.

In practical devices, charge build-up sometimes affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes:

# C

d

Q

d

V

{\displaystyle C= \frac{\mathrm{d}Q}{\mathrm{d}V}}

In the hydraulic analogy, charge carriers flowing through a wire are analogous to water flowing through a pipe. A capacitor is like a rubber membrane sealed inside a pipe. Water molecules cannot pass through the membrane, but some water can move by stretching the membrane. The analogy clarifies a few aspects of capacitors:

* *The current alters the charge on a capacitor*, just as the flow of water changes the position of the membrane. More specifically, the effect of an electric current is to increase the charge of one plate of the capacitor, and decrease the charge of the other plate by an equal amount. This is just as when water flow moves the rubber membrane, it increases the amount of water on one side of the membrane, and decreases the amount of water on the other side.
* *The more a capacitor is charged, the larger its voltage drop*; i.e., the more it "pushes back" against the charging current. This is analogous to the more a membrane is stretched, the more it pushes back on the water.
* *Charge can flow "through" a capacitor even though no individual electron can get from one side to the other.* This is analogous to water flowing through the pipe even though no water molecule can pass through the rubber membrane. The flow cannot continue in the same direction forever; the capacitor experiences dielectric breakdown, and analogously the membrane will eventually break.
* The *capacitance* describes how much charge can be stored on one plate of a capacitor for a given "push" (voltage drop). A very stretchy, flexible membrane corresponds to a higher capacitance than a stiff membrane.
* A charged-up capacitor is storing potential energy, analogously to a stretched membrane.

### Inductors

An electric current flowing through a conductor generates a magnetic field surrounding it. The  magnetic flux linkage

Φ

B

{\displaystyle \Phi\_\mathbf{B}}

 generated by a given current

I

{\displaystyle I}

 depends on the geometric shape of the circuit. Their ratio defines the inductance

L

{\displaystyle L}

. Thus

L
:=

Φ

B

I

{\displaystyle L := \frac{\Phi\_\mathbf{B}}{I}}

.
The inductance of a circuit depends on the geometry of the current path as well as the magnetic permeability of nearby materials. An inductor is a component consisting of a wire or other conductor shaped to increase the magnetic flux through the circuit, usually in the shape of a coil or helix. Winding the wire into a coil increases the number of times the magnetic flux lines link the circuit, increasing the field and thus the inductance. The more turns, the higher the inductance. The inductance also depends on the shape of the coil, separation of the turns, and many other factors. By adding a "magnetic core" made of a ferromagnetic material like iron inside the coil, the magnetizing field from the coil will induce magnetization in the material, increasing the magnetic flux. The high permeability of a ferromagnetic core can increase the inductance of a coil by a factor of several thousand over what it would be without it.

Any change in the current through an inductor creates a changing flux, inducing a voltage across the inductor. By Faraday's law of induction, the voltage induced by any change in magnetic flux through the circuit is given by

E

=
−

d

Φ

B

d
t

{\displaystyle \mathcal{E} = -\frac{d\Phi\_\mathbf{B}}{dt}}

.
Reformulating the definition of

L

{\displaystyle L}

 above, we obtain

Φ

B

=
L
I

{\displaystyle \Phi\_\mathbf{B} = LI}

.
It follows, that

E

=
−

d

Φ

B

d
t

=
−

d

d
t

(
L
I
# )
−
L

d
I

d
t

{\displaystyle \mathcal{E} = -\frac{d\Phi\_\mathbf{B}}{dt} = -\frac{d}{dt}(LI) = -L\frac{dI}{dt}}

.
for

L

{\displaystyle L}

 independent of time.

So inductance is also a measure of the amount of electromotive force (voltage) generated for a given rate of change of current. For example, an inductor with an inductance of 1 henry produces an EMF of 1 volt when the current through the inductor changes at the rate of 1 ampere per second. This is usually taken to be the constitutive relation (defining equation) of the inductor.

The dual of the inductor is the capacitor, which stores energy in an electric field rather than a magnetic field. Its current–voltage relation is obtained by exchanging current and voltage in the inductor equations and replacing *L* with the capacitance *C*.

The effect of an inductor in a circuit is to oppose changes in current through it by developing a voltage across it proportional to the rate of change of the current. An ideal inductor would offer no resistance to a constant direct current; however, only superconducting inductors have truly zero electrical resistance.

The relationship between the time-varying voltage *v*(*t*) across an inductor with inductance *L* and the time-varying current *i*(*t*) passing through it is described by the differential equation:

v
(
t
# )
L

d
i
(
t
)

d
t

{\displaystyle v(t) = L \frac{di(t)}{dt}}

When there is a sinusoidal alternating current (AC) through an inductor, a sinusoidal voltage is induced. The amplitude of the voltage is proportional to the product of the amplitude (*I*P) of the current and the frequency (*f*) of the current.

i
(
t
)

=

I

P

sin
⁡
(
ω
t
)

d
i
(
t
)

d
t

=

I

P

ω
cos
⁡
(
ω
t
)

v
(
t
)

=
L

I

P

ω
cos
⁡
(
ω
t
)

{\displaystyle \begin{align}
 i(t) &= I\_\mathrm P \sin(\omega t) \\
 \frac{di(t)}{dt} &= I\_\mathrm P \omega \cos(\omega t) \\
 v(t) &= L I\_\mathrm P \omega \cos(\omega t)
\end{align}}

In this situation, the phase of the current lags that of the voltage by π/2 (90°). For sinusoids, as the voltage across the inductor goes to its maximum value, the current goes to zero, and as the voltage across the inductor goes to zero, the current through it goes to its maximum value.

If an inductor is connected to a direct current source with value *I* via a resistance *R* (at least the DCR of the inductor), and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an exponential decay:

i
(
t
# )
I

e

−

R
L

t

{\displaystyle i(t) = I e^{-\frac{R}{L}t}}

## Ohm's law

**Ohm's law** states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

# I

V
R

,

{\displaystyle I = \frac{V}{R},}

where *I* is the current through the conductor in units of amperes, *V* is the voltage measured *across* the conductor in units of volts, and *R* is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the *R* in this relation is constant, independent of the current. Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law, these are called non-ohmic.

In circuit analysis, three equivalent expressions of Ohm's law are used interchangeably:

# I

V
R

or

# V
I
R

or

# R

V
I

.

{\displaystyle I = \frac{V}{R} \quad \text{or}\quad V = IR \quad \text{or} \quad R = \frac{V}{I}. }

Each equation is quoted by some sources as the defining relationship of Ohm's law,
or all three are quoted, or derived from a proportional form,
or even just the two that do not correspond to Ohm's original statement may sometimes be given.

The interchangeability of the equation may be represented by a triangle, where V (voltage) is placed on the top section, the I (current) is placed to the left section, and the R (resistance) is placed to the right. The line that divides the left and right sections indicates multiplication, and the divider between the top and bottom sections indicates division (hence the division bar).

### Resistive circuits

Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value *R*. In a schematic diagram the resistor is shown as a zig-zag symbol. An element (resistor or conductor) that behaves according to Ohm's law over some operating range is referred to as an *ohmic device* (or an *ohmic resistor*) because Ohm's law and a single value for the resistance suffice to describe the behavior of the device over that range.

Ohm's law holds for circuits containing only resistive elements (no capacitances or inductances) for all forms of driving voltage or current, regardless of whether the driving voltage or current is constant (DC) or time-varying such as AC. At any instant of time Ohm's law is valid for such circuits.

Resistors which are in *series* or in *parallel* may be grouped together into a single "equivalent resistance" in order to apply Ohm's law in analyzing the circuit.

### Reactive circuits

When reactive elements such as capacitors or inductors are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law (as defined above) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance ("C") or inductance ("L").

Equations for time-invariant AC circuits take the same form as Ohm's law. However, the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials.

In this approach, a voltage or current waveform takes the form

A

e

s
t

{\displaystyle Ae^{st}}

, where *t* is time, *s* is a complex parameter, and *A* is a complex scalar. In any linear time-invariant system, all of the currents and voltages can be expressed with the same *s* parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.

The complex generalization of resistance is impedance, usually denoted *Z*; it can be shown that for an inductor,

# Z
s
L

{\displaystyle Z = sL\,}

and for a capacitor,

# Z

1

s
C

.

{\displaystyle Z = \frac{1}{sC}.}

We can now write,

# V
I
⋅
Z

{\displaystyle \boldsymbol{V} = \boldsymbol{I} \cdot \boldsymbol{Z}}

where ***V*** and ***I*** are the complex scalars in the voltage and current respectively and ***Z*** is the complex impedance.

This form of Ohm's law, with *Z* taking the place of *R*, generalizes the simpler form. When *Z* is complex, only the real part is responsible for dissipating heat.

In the general AC circuit, *Z* varies strongly with the frequency parameter *s*, and so also will the relationship between voltage and current.

For the common case of a steady sinusoid, the *s* parameter is taken to be

j
ω

{\displaystyle j\omega}

, corresponding to a complex sinusoid

A

e

j
ω
t

{\displaystyle Ae^{\mbox{ } j \omega t}}

. The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars.