Introductio of circuit element

Sep. 222017

Tamzid’s Electrical Blog

Charge: Charge Charge is an electrical property of the atomic particles of which matter consists, measured in coulombs (C). # Electric charge is mobile ; i,e, it can be transferred from one place to another, where it can be converted to another form of energy. # The ha ge e o a ele t o is egati e a d e ual i ag itude to .6× − 9C, hile a p oto a ies a positive charge of the same magnitude as the electron. The presence of equal numbers of protons and electrons leaves an atom neutrally charged. # The only charges that occur in nature are integral multiples of the electronic charge, e = 1.6×10^(−19) C. # The law of conservation of charge states that charge can neither be created nor destroyed, only transferred. Thus the algebraic sum of the electric charges in a system does not change. # Alike charges repeal and opposite charges attract each other.

Current: Current Electric current is the time rate of change of charge, measured in amperes (A).

The relationship between current i, charge q, and time t is given by

The di e tio of u e t flo is o e tio all take as the di e tio of positi e ha ge

o e e t.

1

Tamzid’s Electrical Blog

Sep. 222017

Direct Current: A direct current (dc) is a current that remains constant with time.

By convention the symbol I is used to represent dc current. The capital letter I was chosen from the French word for current, intensit´

Alternating Current: An alternating current (ac) is a current that varies sinusoidally with time.

By convention the symbol i is used to represent ac current.

Voltage: Voltage o pote tial diffe e e is the e e g required to move a unit charge through an element, measured in volts (V).

The voltage between two points a and b in an electric circuit is given by,

olt = joule/ oulo

=

e to − ete / oulo

# A constant voltage is called a dc voltage and is represented by V, whereas a sinusoidally time-varying voltage is called an ac voltage and is represented by v.

# A dc voltage is commonly produced by a battery and ac voltage is produced by an electric generator

Power: Power is the time rate of expanding or absorbing energy, measured in watts (W).

2

Tamzid’s Electrical Blog

Sep. 222017

Mathematically,

# The power absorbed ar supplied by an element is the product of the voltage across the element and the current through it. # If current enters the positive terminal of the voltage then p = +vi and if current enters the negative te i al of the oltage the p = − i. # p = +vi implies that the element is absorbing power. # p = − i implies that the element is supplying power.

Energy: Energy is the capacity to do work, measured in joules (J).

The energy absorbed or supplied by an element from time t0 to time t is given by

Electric energy is measured in watt-hours(Wh) , where 1Wh = 3600J

Circuit Elements There are two types of circuit elements: 1. Active circuit elements 2. Passive circuit elements Active circuit elements

3

Sep. 222017

Tamzid’s Electrical Blog

Active circuit elements are capable of generating energy such as, generators, batteries, operational a pliďŹ e s et .

Passive circuit elements Passive circuit elements are not capable of generating energy such as, resistors, capacitors, inductors etc.

Most important active elements are voltage and current sources which deliver power to the circuit connected to them.

There are two kinds of sources.

1. Independent sources 2. Dependent sources

Independent source A ideal i depe de t sou e is a a ti e ele e t that p o ides a spe iďŹ ed oltage a completely independent of other circuit elements.

Independent voltage source

u e t that is

An ideal independent voltage source delivers to the circuit

whatever current is necessary to maintain its terminal voltage. Example: Generators and batteries.

Independent current source

An ideal independent current source delivers to the circuit

whatever voltage is necessary to maintain the designated current.

Dependent source An ideal dependent source is an active element in which the source quantity is controlled by another voltage or current.

Dependent sources are of four kinds:

4

Tamzid’s Electrical Blog

Sep. 222017

1. Voltage-controlled voltage source (VCVS) 2. Current-controlled voltage source (CCVS) 3. Voltage-controlled current source (VCCS) 4. Current-controlled current source (CCCS)

Application Dependent sources are used for modeling elements such as transistors, operational a plifie s a d i teg ated i uits.

Ideal voltage controlled voltage source The equation for the supplied voltage Vs is given by

where Vx is the controlling voltage and µ is a multiplying constant that is dimensionless.

Ideal current controlled voltage source The equation for the supplied voltage Vs is given by

where i is the o t olli g u e t a d the

ultipl i g o sta t, ρ has the di e sio

olts pe a pe e.

Ideal voltage controlled current source The equation for the supplied current is is given by

5

Sep. 222017

Tamzid’s Electrical Blog

where V is the o t olli g oltage a d the

ultipl i g o sta t α has a di e sio of a pe e pe

olt.

Ideal current controlled current source The equation for the supplied current is is given by

where ix is the controlling current and the multiplying o sta t, β is di e sio less

Resistor The i uit ele e t used to i pede the flo of u e t o , called resistor.

o e spe ifi all , the flo of ele t i

ha ge is

The apa it of esisto to i pede the flo of u e t o , o e spe ifi all , the flo of ele t i alled esista e,e p essed R a d easu ed i oh s Ω .

ha ge is

Resistance

6

Tamzid’s Electrical Blog

Sep. 222017

he e, ρ = Resisti it of the

ate ial i oh -meters

l = Length of the material A = Area of cross section of the material.

Short Circuit A short circuit is a circuit element with resistance approaching zero i,e, R = 0. For a short circuit v = iR = 0.

Open Circuit A ope

i uit is a i uit ele e t ith esista e app oa hi g i fi it i,e, R = ∞. For an open circuit,

Fig. (a) short circuit and (b) open circuit

7

Sep. 222017

Tamzid’s Electrical Blog

Types of Resistors 1. Fixed i,e, their resistance is constant.

2. Variable i,e, their resistance is adjustable. Such as, potenitometer or pot.

Fig. Symbol for variable resistance.

Inductors Inductor Inductor is a passive ele e t desig ed to sto e e e g i its o du ti g i e. I du to s a e fi ed o a ia le. The o e a

ag eti field. It o sists of a oil of e ade of i o , steel, plasti , o ai .

Application 1. Electronics and power system 2. Power supplies, transformers, radios, TVs, radars and electric motors.

Fig. Symbol for inductor (a) air-core, (b) iron core, (c) variable iron-core.

Types and Configurations I du to s a e of t o t pes: fi ed a d a ia le. A i du to solenoidal, toroidal etc

a ha e diffe e t o figu atio s such as

8

Tamzid’s Electrical Blog

Sep. 222017

Fig. Va ious i du to o figu atio s a sole oidal

to oidal

Inductance I du ta e is the p ope t he e through it, measured in henrys (H).

a i du to e hi its oppositio to the ha ge of u e t flo i g

The inductance of a coil varies directly with the magnetic properties of the coil. Ferromagnetic materials, the efo e, a e f e ue tl e plo ed to i ease the i du ta e i easi g the flu li ki g the oil.

The inductance of an inductor is given by

where, N = Number of turns µ = Permeability of the core A = Cross section of the core l = length of the core Voltage-current relationship of an inductor is given by

9

Tamzid’s Electrical Blog

Sep. 222017

The power delivered to the inductor is

The energy stored in the inductor is given by

# When the current through an inductor is not changing with time i,e, dc current (di/dt = 0), the voltage across the inductor is zero.Thus, inductor is an short circuit to dc.

# An inductor resists an abrupt change in the current through it. A discontinuous e ui es i fi ite oltage, change instantaneously

change in current hi h is ph si all i possi le. Co e sel , oltage a oss a i du to a

# The ideal inductor does not dissipate energy. It takes power from the circuit when storing energy in its field a d returns previously stored energy when delivering power to the circuit # A real, non-ideal inductor has a series winding resistance as it is made of conducting materials, which has some resistance. The non-ideal inductor also has a winding capacitance which is due to the capacitive coupling between the conducting coils.

Capacitors Capacitor Capa ito is a passi e ele e t desig ed to sto e e e g i its ele t i field. It o sists of t o o du ti g plates separated by an insulator or dielectric. The plate may be aluminium foil while the dielectric may be air, ceramic, paper or mica.

Application 1. Tuning circuits of radio receivers 2. Dynamic memory elements in computer system 3. To block dc, pass ac, shift phase, store energy, start motors and suppress noise.

10

Sep. 222017

Tamzid’s Electrical Blog

Types Two types of capacitors are available. Such as 1. Fixed capacitor 2. Variable capacitor or trimmer capacitor or padder

Fig. A capacitor with applied voltage v.

When a voltage source is connected to the capacitor,the source deposits a positive charge +q on one plate a d a egati e ha ge − o the othe . The a ou t of ha ge sto ed, ep ese ted , is di e tl proportional to the applied voltage so that q = Cv, where, C is known as the capacitance.

Capacitance

Capacitance is the ratio of the charge on one plate of a capacitor to the voltage die e e et ee the t o plates, easu ed i fa ads F . fa ad = oulo / olt

For parallel plate capacitor, the capacitance is given by

11

Sep. 222017

Tamzid’s Electrical Blog

where,

= Permittivity of the dielectric material between the plates A = Surface area of each plate d = Distance between the plates

Current-voltage relationship of a capacitor is given by

The instantaneous power delivered to the capacitor is

The energy stored in the capacitor is given by

# When the voltage across a capacitor is not changing with time i,e, dc voltage (dv/dt = 0), the current through the capacitor is zero.Thus, capacitor is an open circuit to dc.However, if a battery (dc voltage) is connected across a capacitor, the capacitor charges. # A capacitor resists an abrupt change in the voltage across it. A discontinuous change in voltage e ui es i fi ite u e t, hi h is ph si all i possi le. Co e sel , u e t th ough a apa ito a change instantaneously. # The ideal capacitor does not dissipate energy. It takes power from the circuit when storing energy in its field a d etu s p e iousl sto ed e e g he deli e i g po e to the i uit. # A real, non-ideal capacitor has a parallel-model leakage resistance.The leakage resistance may be as high as MΩ a d a e egle ted fo ost p a ti al appli atio s.

OHM’s Law: In 1826 George Simon Ohm stated a law as “ the current in a metal conductor which is maintained at a constant tem Fig. Current flowing through a conductor.

12

Sep. 222017

Tamzid’s Electrical Blog

13

Sep. 222017

Tamzid’s Electrical Blog

14