LECTURE 3 4

BS in Electrical Engineering

Presented By:

Contents

 _{Electric Charge}  _{Electric current}  _Voltage

 _Power

_{Passive Sign Convention}

 _Resistance

 _{Laws of Resistance}  _{Unit of Resistivity}  _Conductance

Systems of UNITS

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Quantity Basic Unit Symbol

Length meter m

Mass kilogram kg

Time second s

Electric current ampere A

Thermodynamic

Temperature kelvin K

Luminous

Electric Charge

_{Electric charge is the physical}

property of matter that causes it to experience a force when placed in an electromagnetic field.

 _{There are two types of electric} charges: positive and negative.

 _{Positively charged substances are repelled} from other positively charged substances, but attracted to negatively charged

substances.

_{Negatively charged substances are}

repelled from negative and attracted to

Electric Charge

 _{An object is negatively charged if it has an excess}

of electrons, and is otherwise positively charged or uncharged.

 _{The electric charge is a fundamental conserved}

property of some subatomic particles, which determines their electromagnetic interaction.

 _{Electrically charged matter is influenced by, and}

produces, electromagnetic fields. The interaction between a moving charge and an

electromagnetic field is the source of

Electric Current

_{An electric current is a flow of electric}

charge.

 _{In electric circuits this charge is often}

carried by moving electrons in a wire.

_{It can also be carried by ions in}

an electrolyte, or by both ions and electrons such as in a plasma.

Electric Current

_{The particles that carry the charge in an} electric current are called charge carriers. _{In metals, one or more electrons from each}

atom are loosely bound to the atom, and can move freely about within the metal.  _{These conduction electrons are the}

charge carriers in metal conductors.

SI Unit of Electric Current

_{The SI unit for measuring an electric}

current is the ampere, which is the flow of electric charge across a surface at the rate of one coulomb per second.

_{Electric current is measured using a device}

called an ammeter.

_{The conventional symbol for current is I}

Voltage

 _{The voltage between two points is equal} to the work done per unit of

charge against a static electric field to

move the charge between two points and is measured in units

of volts (a joule per coulomb).

_{It must take some work or energy for the} charge to move between 2 points in a

circuit say from point A to point B.

Electric Potential

 _{An electric potential (also called the} electric

field potential or the electrostatic potential) is the amount of electric potential energy that a unitary point electric charge would have if located at any point in space, and is equal to the work done by an electric field in carrying a unit positive charge from infinity to that point

 _{The volt (symbol: V) is the derived}

unit for electric potential, electric potential

difference (voltage), and electromotive force. The volt is named in honour of the Italian

physicist Alessandro Volta (1745–1827), who invented the voltaic pile, possibly the first chemical battery.

Electric Power

_{Power is a measure of how much work can} be performed in a given amount of time.

_{Power is a measure of how rapidly a} standard amount of work is done.

 _{The unit of power is the joule per second (J/s),}

known as the watt in honour of James Watt, the eighteenth-century developer of the steam

engine.

The instantaneous electrical power P delivered to a component is given by

where

P(t) is the instantaneous power, measured in watts (joules per second)

V(t) is the potential difference (or voltage drop) across the component, measured in volts

I(t) is the current through it, measured in amperes ₁₃

Electric Power

_{If the component is a resistor with}

Passive Sign Convention

 _{The passive sign convention (PSC) is a sign}

convention or arbitrary standard rule adopted universally by the electrical engineering

community for defining the sign of electric power in an electric circuit

 _{The convention defines electric power flowing}

out of the circuit into an electrical

component as positive, and power flowing into the circuit out of a component as negative.

 _{So a passive component which consumes}

power, such as an appliance or light bulb, will have positive power dissipation,

 _{while an active component, a source of power}

such as an electric generator or battery, will have negative power dissipation. This is the

standard definition of power in electric circuits.

Active and passive

components

_{From the standpoint of power}

flow, electrical components in a circuit can be divided into two types

 _{Active and}

Passive Component

 _{In a} load _or passive _{component, such as a light}

bulb, resistor, or electric motor, electric

current (flow of positive charges) moves through the device under the influence of the voltage in the direction of lower electric potential, from the positive terminal to the negative.

 _{So work is done by the charges on the}

component; potential energy flows out of the

charges; and electric power flows from the circuit into the component, where it is converted to

some other form of energy such as heat or mechanical work.

Active Components

 _{In a} source _or active _{component, such as}

a battery or electric generator, current is forced to move through the device in the direction of greater electric potential energy, from the

negative to the positive voltage terminal.

 _{This increases their potential energy, so electric}

power flows out of the component into the circuit. 

 _{Work must be done} on _{the moving charges by}

Passive Sign Convention

Current direction and voltage polarity play a major role in determining the sign of power.

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The voltage polarity and current direction must conform with those shown in Fig in order for the power to have a positive sign. This is known as

Conductance

_{The ease with which an electric current} passes

_{Conductance (G) is reciprocal of resistance}  _{Whereas resistance of a conductor}

measures the opposition which it offers to the flow of current, the conductance

measures the inducement which it offers to its flow

Conductivity

_{The conductivity is defined as the} ration of the current density of J to the electric Field E:

Resistance

 _{It may be defined as the property of a substance}

due to which it opposes (or restricts) the flow of electricity (i.e., electrons) through it.

 _{Metals (as a class), acids and salts solutions are}

good conductors of electricity.

 _{Amongst pure metals, silver, copper and}

Resistance

 _{The presence of a large number of free or} loosely-attached electrons in their atoms.  _{These vagrant electrons assume a}

directed motion on the application of an electric potential difference.

 _{These electrons while flowing pass}

through the molecules or the atoms of the conductor, collide and other atoms and

electrons, thereby producing heat.

Resistance

 _{Those substances which offer relatively greater}

difficulty or hindrance to the passage of these

electrons are said to be relatively poor conductors of electricity like

 _Bakelite,  _mica,  _glass,  _rubber,

The Unit of Resistance

_{The practical unit of resistance is ohm.} _Definition

“A conductor is said to have a resistance of one ohm if it permits one ampere current to flow through it when one volt is impressed across its terminals”.

The Unit of Resistance

_{For insulators whose resistances are very} high, a much bigger unit is used i.e.,

mega-ohm = 106 ohm (the prefix ‘mega’ or mego meaning a million) or kilo-ohm = 103 ohm (kilo means thousand). In the

case of very small resistances, smaller units like milli-ohm = 10-3 ohm or

Laws of Resistance

_{The resistance R offered by a conductor} depends on the following factors :

 _{It varies directly as its length, l.}

 _{It varies inversely as the cross-section A of} the conductor.

 _{It depends on the nature of the material.}  _{It also depends on the temperature of the}

conductor.

Laws of Resistance

_{Neglecting the last factor for the time} being, we can say that

R ∝ l A or R = l A ρ ...(i)

Laws of Resistance

Laws of Resistance

If in Eq. (i), we put

l = 1 metre and A = 1 metre2, then R = ρ (Fig. 1.4)

Hence, specific resistance of a material may be defined as the resistance between the

Units of Resistivity

_{From Eq. (i), we have ρ = AR l}

_{Hence, the unit of resistivity is ohm-metre} (Ω-m).

Effect of Temperature on Resistance

The effect of rise in temperature is :

 _{To increase the resistance of pure metals. The}

increase is large and fairly regular for normal ranges of temperature. The temperature/resistance graph is a

straight line .As would be presently clarified, metals have a positive temperature co-efficient of resistance.

 _{To increase the resistance of alloys, though in their}

case, the increase is relatively small and irregular. For

some high-resistance alloys like Eureka (60% Cu and 40% Ni) and manganin, the increase in resistance is (or can be made) negligible over a considerable range of temperature.

 _{To decrease the resistance of electrolytes, insulators}

(such as paper, rubber, glass, mica etc.) and partial

conductors such as carbon. Hence, insulators are said to possess a negative temperature-coefficient of resistance

Temperature Coefficient of Resistance

Resistance in Series

_{When some conductors having resistances} R1, R2 and R3 etc. are joined end-on-end, they are said to be connected in series.

 _{It can be proved that the equivalent}

resistance or total resistance between two points is equal to the sum of the three

individual resistances.

Resistance in Series

 _{Being a series circuit, it should be} remembered that

a) current is the same through all the three conductors

b) But voltage drop across each is different due to its different resistance and is

given by Ohm’s Law and

c) sum of the three voltage drops is equal to the voltage applied across the three

Resistance in Series

 _{V = V1 + V2 + V3 = IR1 + IR2 + IR3 —} Ohm’s Law

 _{But V = IR where R is the equivalent}

resistance of the series combination. ∴ IR = IR1 + IR2 + IR3 or

 _{R= R1 + R2 + R3}

Main Characteristics of Series Circuit

_{The main characteristics of a series circuit} are :

a) same current flows through all parts of the circuit.

b) different resistors have their individual voltage drops.

c) voltage drops are additive.

d) applied voltage equals the sum of different voltage drops.

Resistance in Parallel

_{A parallel circuit is a circuit in which the} resistors are arranged with their heads connected together, and their tails

connected together.

_{The current in a parallel circuit breaks up,} with some flowing along each parallel

branch and re-combining when the branches meet again.

_{The voltage across each resistor in parallel} is the same.

Resistance in Parallel

_{Three resistances, as joined in Fig are said} to be connected in parallel. In this case  _{p.d. across all resistances is the same}

 _{current in each resistor is different and is} given by Ohm’s Law

Resistance in Parallel

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 _{The total resistance of a set of resistors in parallel is found by adding up the}

reciprocals of the resistance values, and then taking the reciprocal of the total:

Main characteristics of a Parallel Circuit

The main characteristics of a parallel circuit are :

 _{same voltage acts across all parts of the} circuit

 _{different resistors have their individual} current.

Kirchhoff’s Laws

_{These laws are more comprehensive than} Ohm’s law and are used for solving

electrical networks which may not be readily solved by the latter. Kirchhoff’s laws, two in number, are particularly

useful

 _{In determining the equivalent resistance of} a complicated network of conductors and  _{For calculating the currents flowing in the}

various conductors.

Kirchhoff’s Point Law or Current Law (KCL)

_{It states as follows :}

“In any electrical network, the algebraic sum of the currents meeting at a point (or

junction) is zero”

_{Put in another way, it simply means that}

the total current leaving a junction is equal to the total current entering that junction. _{It is obviously true because there is no}

(KCL)

_{Consider the case of a few conductors}

meeting at a point A as in Fig

 _{Some conductors have currents leading to}

point A, whereas some have currents leading away from point A.

KCL

_{Assuming the incoming currents to be}

positive and the outgoing currents negative, we have

I1 + (− I2) + (− I3) + (+ I4) + (− I5) = 0 or I1 + I4 − I2 − I3 − I5 = 0

or I1 + I4 = I2 + I3 + I5

or incoming currents = outgoing currents

_{Similarly, in Fig (b) for node A}

Kirchhoff’s Mesh Law or Voltage Law (KVL)

_{It states as follows :}

“The algebraic sum of the products of currents and resistances in each of the

conductors in any closed path (or mesh) in a network plus the algebraic sum of the

e.m.fs. in that path is zero”. In other words,

 _{Σ IR + Σ e.m.f. = 0 ...round a mesh}

_{It should be noted that algebraic sum is} the sum which takes into account the polarities of the voltage drops.

KVL

_{The basis of this law is this :}

If we start from a particular junction and go round the mesh till we come back to the

starting point, then we must be at the same potential with which we started.

_{Hence, it means that all the sources of}

e.m.f. met on the way must necessarily be equal to the voltage drops in the

Kirchhoff’s Laws

Examples

_{We will apply KVL to find Vs.}

Starting from point A in the clockwise direction and using the sign convention

+Vs + 10 − 20 − 50 + 30 = 0

∴ Vs = 30 V

Examples

 _{Initially, one may not be clear regarding}

the solution of this question.

 _{One may think of Kirchhoff’s laws or mesh}

analysis etc. But a little thought will show that the question can be solved by the

simple application of Kirchhoff’s voltage law.

 _{Taking the outer closed loop ABCDEFA and}

applying KVL to it, we get

 _{− 16 × 3 − 4 × 2 + 40 − V1 = 0 ;}

∴ V1 = −16 V