' D A 5 D ' D . ' E 3 9 4 1 E * 3 9 ) H E - ' + G · Title: ï¿½ï¿½Microsoft Word - ' D A 5 D...

Ch 15 Capacitors (C) & Inductors (L)

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THE ELECTRIC FIELDelectric field is represented by electric flux lines, which are drawn to indicate the strength

of the electric field at any point around the charged body; that is, the denser the lines of

flux, the stronger the electric field. In Fig. (1).

Fig.(1)

The symbol for electric flux is the Greek letter ѱ (psi). The flux per unit area (flux

density) is represented by the capital letter (D) and is determined by:

The larger the charge (Q in coulombs) , the greater the number of flux lines extending or

terminating per unit area, independent of the surrounding medium. Twice the charge will

produce twice the flux per unit area. The two can therefore be equated:

the electric field strength( E ) at a point is the force acting on a unit positive charge at

that point; that is,


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Electric flux lines always extend from a positively charged body to a negatively charged

body, always extend or terminate perpendicular to the charged surfaces, and never

intersect.

For two charges of similar and opposite polarities, the flux distribution would appear as

shown in Fig. (2) .

Fig(2): Electric flux distribution: (a) like charges; (b) opposite charges.

1- CAPACITOR: This element, constructed simply of two parallel conducting plates

separated by an insulating material (in this case, air), is called a capacitor.

CHARGING OF CAPACITANCEtwo parallel plates of a conducting material separated by an air gap have been connected

through a switch and a resistor to a battery fig. (3) . If the parallel plates are initially

uncharged and the switch is left open, no net positive or negative charge will exist on

either plate. The instant the switch is closed, however, electrons are drawn from the upper

plate through the resistor to the positive terminal of the battery. There will be a surge of


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current at first, limited in magnitude by the resistance present. The level of flow will then

decline, as will be demonstrated in the sections to follow. This action creates a net positive

charge on the top plate. Electrons are being repelled by the negative terminal through the

lower conductor to the bottom plate at the same rate they are being drawn to the positive

terminal. This transfer of electrons continues until the potential difference across the

parallel plates is exactly equal to the battery voltage. The final result is a net positive

charge on the top plate and a negative charge on the bottom plate,

Fig.(3) Fundamental charging of capacitor

Capacitance is a measure of a capacitor’s ability to store charge on its plates.

Ideal capacitance

the ideal situation, the capacitor do not dissipate energy as does the resistor but store it in

a form that can be returned to the circuit .

CAPACITORS IN SERIES (fig.4)

Fig.(4)

For capacitors in series, the charge is the same on each capacitor


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--------------------(1)

Using Eq. (1) and dividing both sides by( Q ) yields:

Or

CAPACITORS IN PARALLEL (fig. 5):

Fig.(5)

capacitors in parallel, as shown in Fig. (5) the voltage is the same across each capacitor,

and the total charge is the sum of that on each capacitor.


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which is similar to the manner in which the total resistance of a series circuit is found.

EXAMPLE (1): For the circuit of Fig. (6):

a. Find the total capacitance.

b. Determine the charge on each plate.

c. Find the voltage across each capacitor.

Fig(6)


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EXAMPLE (2): For the network of Fig. (7):

a. Find the total capacitance.

b. Determine the charge on each plate.

c. Find the total charge.

Fig(7)


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Series and parallel combinations

EXAMPLE (3) Find the voltage across and charge on each capacitor for the network of

Fig. (8).

Fig(8 )

An equivalent circuit (Fig. 8-a) has


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Fig.(8-a)


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2- INDUCTOR (L)Inductors are coils of various dimensions designed to introduce specified amountsof inductance into a circuit. The inductance of a coil varies directly with themagnetic properties of the coil.fig(9)

The inductance of the coils of Fig. (9) can be found using the following equation:

where (N) represents the number of turns;( µ), the permeability of the core recall that( µ)

is not a constant but depends on the level of ; (A ) the area

of the core in square meters; and( l ) , the length of the core in meters.

The inductance of a coil is also a measure of the change in flux linking a coil due to a

change in current through the coil; that is:

Fig.(9) Inductor configurations


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SELF-INDUCTANCEThe ability of a coil to oppose any change in current is a measure of theself-inductance L of the coil.INDUCED VOLTAGE

the magnitude of the voltage across an inductor is directly related to the inductance (L)and

the instantaneous rate of change of current through the coil.,

the symbol (eL)is appropriate for the induced voltage. Or we can use the symbol(vL).

coil:ctualA

every inductor are a resistance equal to the resistance of the turns and a stray capacitance

due to the capacitance between the turns of the coil. the equivalent circuit for the inductor

is as shown in Fig. (10). However, for most applications, the stray capacitance appearing

in Fig. (10) can be ignored, resulting in the equivalent model of Fig. (11) The resistance

RL can play an important role in the analysis of networks with inductive elements.

Fig(10) equivalent circuit for an inductor.

Fig(11) Practical equivalent circuit for an inductor


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Ideal coil : an ideal coil mean that the coil do not dissipate energy as does the resistor

but store it in a form that can be returned to the circuit whenever required by the circuit

design. fig(12).

INDUCTORS IN SERIES

INDUCTORS IN PARALLEL

Fig. (12) An ideal coil


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POWER & ENERGY STORED BY AN INDUCTORThe ideal inductor, like the ideal capacitor, does not dissipate the electrical energy

supplied to it. It stores the energy in the form of a magnetic field.

PL=VL*IL (watt)

PL: the power (W)

VL : induced voltage (V)

IL : current through the coil (I)

W: energy (J) L: self inductance (H) Im : maximum current through the coil

Example(4) : Reduce the network of Fig.(13) to its simplest form.

Fig.(13)

The inductors L2 and L3 are equal in value and they are in parallel, resulting in an

equivalent parallel value of :

= 2// 3


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=1.2 ∗ 1.2

1.2 + 1.2

= 0.6 H

The reduced equivalent network appears in Fig.(14)

Fig. (14) Equivalent cct. Of network of (13)

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