inductors and capacitors a

Inductors and Capacitors

Passive Elements

Capacitors

Capacitor

Is consists of two conducting plates separated by an insulator (dielectric).

CAPACITANCE – It is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates and measured in Farads

1 Farad = 1 Coulomb/Volt

d

AC

Where: - permittivity of the dielectric material A - surface area of each plates d - distance between the plate

Where: q- charge stored C- Capacitance v- applied voltage

A capacitor is a passive element designed to store energy in its electric field. (Electro static energy)

q = Cv

Voltage and Current Relation

CAPACITORS oppose changes in voltage by drawing or supplying current as they charge or discharge to the new voltage level.

The flow of electrons “through” a capacitor is directly proportional to the rate of change of voltage across the capacitor.

)( 0tVC

dtiV

c

C

dt

dVCi C

C

Energy

The energy stored in the capacitor is:

Where: C - Capacitance

v - Voltage

2

2

1CvW

Important Properties of Capacitor

The capacitor is an open circuit to DC.

Important Properties of Capacitor

The voltage on capacitor cannot change abruptly.

(a) is ALLOWED (b) NOT ALLOWED ( an abrupt change is not possible)

Waveform of the Voltage across the capacitor:

Capacitors in Series

The equivalent capacitance of series-connected capacitors is the reciprocal of the sum of the reciprocal of the individual capacitance.

Capacitors in Parallel

The equivalent capacitance of N-parallel connected capacitors is the sum of the individual capacitance.

Problems:

1.

Problems:

2.

Problems:

3.

4.

Problems: 5.

6.

Change in voltage as shown in the figure :

0V – 50V between 0 sec. to 1 sec ( 0 < t < 1 )

50V – (-50V) between 1 sec. to 3 sec ( 1 < t < 3 )

(-50V) – 0V between 3 sec. to 4 sec ( 3 < t < 4 )

Note: The line equation is Y = mX + b; Therefore: V(t) = mt + b

7.

Recall that:

(a) is ALLOWED (b) NOT ALLOWED ( an abrupt change is not possible)

Change of voltage as shown in the figure :

0V – 50V between 0 sec. to 1 sec ( 0 < t < 1 )

50V – (-50V) between 1 sec. to 3 sec ( 1 < t < 3 )

(-50V) – 0V between 3 sec. to 4 sec ( 3 < t < 4 )

0 < t < 1

V(t) = mt + b

When t = 0, V(t) = 0V

0 = m*0 + b

b = 0

t = 1, V(t) = 50V

50 = m*1 + 0

m = 50

Voltage equation

w/ respect to time:

V(t) = 50t

1 < t < 3

t = 1;

50 = m*1 + b

t = 3;

-50 = m*3 + b

m = -50

b = 100

V(t) = -50t + 100

Change of voltage as shown in the figure :

0V – 50V between 0 sec. to 1 sec ( 0 < t < 1 )

50V – (-50V) between 1 sec. to 3 sec ( 1 < t < 3 )

(-50V) – 0V between 3 sec. to 4 sec ( 3 < t < 4 )

3 < t < 4

t = 3;

-50 = m*3 + b

t = 4;

0 = m*4 + b

m = 50

b = -200

V(t) = 50t - 200

0 < t < 1

i = 200 (1x10-6) d 50t

dt i = 10 mA

Change of voltage as shown in the figure :

0V – 50V bet. 0 sec. to 1 sec ( 0 < t < 1 )

50V – (-50V) bet. 1 sec. to 3 sec ( 1 < t < 3 )

(-50V) – 0V bet. 3 sec. to 4 sec ( 3 < t < 4 )

Inductors

Inductor

It is a passive element designed to store energy in

its magnetic field. (Electro magnetic energy)

- It is consists of coil of conducting wires.

INDUCTANCE is the property whereby an inductor exhibits opposition to the change of current flowing through it and it is measured in Henrys (H).

l

ANL

2

where: N – number of turns - permeability of the core A – cross-sectional area l - length

INDUCTOR oppose changes in current through them, by dropping a voltage directly proportional to the rate of change of current.

dt

diLVL

)(1

0tidtVL

i tLL

Voltage and Current Relationship

Energy

The energy stored in the inductor is:

Where: L - Inductance

i - current

2

2

1LiW

Important Properties of Inductor

The inductor is a short circuit to dc.

Important Properties of Inductor

The current through an inductor cannot change instantaneously.

Current though an inductor:

a) Allowed b) Not allowable (an abrupt change is not possible)

Inductors in Series

The equivalent inductance of series-connected inductors is the sum of the of the individual inductance.

Inductors in Parallel

The equivalent capacitance of N-parallel connected inductors is the reciprocal of the sum of the reciprocal individual inductance.

Problems:

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Problems:

2.

3.

Problems:

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