ARRDEKTA INSTITUTE OF TECHNOLOGY GUIDED BY. GUIDED BY. Prof.Y.B.Vaghela. Prof.Y.B.Vaghela. Asst.prof in electrical Asst.prof in electrical Department Department

ARRDEKTA INSTITUTE OF ARRDEKTA INSTITUTE OF TECHNOLOGYTECHNOLOGY

GUIDED BY.GUIDED BY. Prof.Y.B.Vaghela.Prof.Y.B.Vaghela.

Asst.prof in electricalAsst.prof in electrical

DepartmentDepartment

PREPARED BY.PREPARED BY. GandhiChandani GandhiChandani

(130930107002) (130930107002) Joshi IshaniJoshi Ishani

(130930107004)(130930107004) Patel Devangi Patel Devangi

(130930107007) (130930107007) Rathwa Vaishali Rathwa Vaishali

(130930109030) (130930109030)

Overview of Circuit Overview of Circuit TheoryTheory

Electrical Electrical circuit elementscircuit elements are idealized are idealized models of physical devices that are models of physical devices that are defined by relationships between defined by relationships between their terminal voltages and their terminal voltages and currents. Circuit elements can have currents. Circuit elements can have two or more terminals.two or more terminals.

An An electrical circuitelectrical circuit is a connection of is a connection of circuit elements into one or more circuit elements into one or more closed loops.closed loops.


Basic quantities are Basic quantities are voltagevoltage, , currentcurrent, and , and powerpower..

The The sign conventionsign convention is important in is important in computing power supplied by or computing power supplied by or absorbed by a circuit element.absorbed by a circuit element.

Circuit elementsCircuit elements can be active or can be active or passive; active elements are passive; active elements are sources.sources.


CurrentCurrent is moving is moving positivepositive electrical electrical charge.charge.

Measured in Amperes (A) = 1 Coulomb/sMeasured in Amperes (A) = 1 Coulomb/s Current is represented by Current is represented by II or or ii.. In general, current can be an arbitrary In general, current can be an arbitrary

function of time.function of time. Constant current is called Constant current is called direct currentdirect current (DC). (DC). Current that can be represented as a Current that can be represented as a

sinusoidal function of time (or in some sinusoidal function of time (or in some contexts a sum of sinusoids) is called contexts a sum of sinusoids) is called alternating currentalternating current (AC). (AC).


VoltageVoltage is electromotive force is electromotive force provided by a source or a potential provided by a source or a potential difference between two points in a difference between two points in a circuit.circuit.

Measured in Volts (V): 1 J of energy Measured in Volts (V): 1 J of energy is needed to move 1 C of charge is needed to move 1 C of charge through a 1 V potential difference.through a 1 V potential difference.

Voltage is represented by Voltage is represented by VV or or vv..


The lower case symbols The lower case symbols vv and and ii are are usuallyusually used to denote voltages used to denote voltages and currents that are functions of and currents that are functions of time.time.

The upper case symbols The upper case symbols VV and and II are are usuallyusually used to denote voltages used to denote voltages and currents that are DC or AC and currents that are DC or AC steady-state voltages and currents.steady-state voltages and currents.


Current has an assumed direction of flow; Current has an assumed direction of flow; currents in the direction of assumed current currents in the direction of assumed current flow have positive values; currents in the flow have positive values; currents in the opposite direction have negative values.opposite direction have negative values.

Voltage has an assumed polarity; volt drops Voltage has an assumed polarity; volt drops in with the assumed polarity have positive in with the assumed polarity have positive values; volt drops of the opposite polarity values; volt drops of the opposite polarity have negative values.have negative values.

In circuit analysis the assumed polarity of In circuit analysis the assumed polarity of voltages are often defined by the direction voltages are often defined by the direction of assumed current flow.of assumed current flow.


PowerPower is the rate at which energy is is the rate at which energy is being absorbed or supplied.being absorbed or supplied.

PowerPower is computed as the product of is computed as the product of voltage and current:voltage and current:

Sign convention: positive power Sign convention: positive power means that energy is being means that energy is being absorbedabsorbed; ; negative power means that power is negative power means that power is being being suppliedsupplied..

VIPtitvtp or


+

-

v(t)

i(t)

• If p(t) > 0, then the circuit element is absorbing power from the rest of the circuit.• If p(t) < 0, then the circuit element is supplying power to the rest of the circuit.

Rest of circuit

Circuit element under consideration


If power is positive into a circuit If power is positive into a circuit element, it means that the circuit element, it means that the circuit element is absorbing power.element is absorbing power.

If power is negative into a circuit If power is negative into a circuit element, it means that the circuit element, it means that the circuit element is supplying power. Only element is supplying power. Only active elementsactive elements (sources) can supply (sources) can supply power to the rest of a circuit.power to the rest of a circuit.

Active and Passive Active and Passive ElementsElements

Active elementsActive elements can generate energy. can generate energy. Examples of active elements are Examples of active elements are

independent and dependent sources.independent and dependent sources. Passive elementsPassive elements cannot generate cannot generate

energy.energy. Examples of passive elements are Examples of passive elements are

resistors, capacitors, and inductors.resistors, capacitors, and inductors. In a particular circuit, there can be In a particular circuit, there can be

active elementsactive elements that absorb power – for that absorb power – for example, a battery being charged.example, a battery being charged.

Independent and Independent and Dependent SourcesDependent Sources

An An independent sourceindependent source (voltage or (voltage or current) may be DC (constant) or current) may be DC (constant) or time-varying; its value does not time-varying; its value does not depend on other voltages or depend on other voltages or currents in the circuit.currents in the circuit. A A dependent sourcedependent source has a value that has a value that depends on another voltage or depends on another voltage or current in the circuit.current in the circuit.

Independent SourcesIndependent Sources

Voltage Source Current Source

tvs tis

Dependent SourcesDependent Sources

+

-

v=f(vx)

Voltage Controlled

Voltage Source (VCVS)

+

-

v=f(ix)

Current Controlled

Voltage Source (CCVS)

Dependent SourcesDependent Sources

I=f(Vx)

Voltage Controlled

Current Source (VCCS)

I=f(Ix)

Current Controlled

Current Source (CCCS)

Passive Lumped Circuit Passive Lumped Circuit ElementsElements

ResistorsResistors

CapacitorsCapacitors

InductorsInductors

R

L

C

Topology of CircuitsTopology of Circuits

A lumped circuit is composed of A lumped circuit is composed of lumped elements (sources, lumped elements (sources, resistors, capacitors, inductors) resistors, capacitors, inductors) and conductors (wires).and conductors (wires).

All the elements are assumed to All the elements are assumed to be lumped, i.e., the entire circuit be lumped, i.e., the entire circuit is of negligible dimensions.is of negligible dimensions.

All conductors are perfect.All conductors are perfect.


A A schematic diagramschematic diagram is an electrical is an electrical representation of a circuit.representation of a circuit.

The location of a circuit element in a The location of a circuit element in a schematic may have no relationship schematic may have no relationship to its physical location.to its physical location.

We can rearrange the schematic and We can rearrange the schematic and have the same circuit as long as the have the same circuit as long as the connections between elements connections between elements remain the same.remain the same.


Example: Schematic of a circuit:Example: Schematic of a circuit:

“Ground”: a reference point where the voltage (or potential) is assumed to be zero.

Topology of CircuitsTopology of Circuits Only circuit elements that are in Only circuit elements that are in

closed loops (i.e., where a current closed loops (i.e., where a current path exists) contribute to the path exists) contribute to the functionality of a circuit.functionality of a circuit. This circuit

element can be removed without affecting functionality. This circuit behaves identically to the previous one.


A A nodenode is an is an equipotential pointequipotential point in a circuit. in a circuit. It is a topological concept – in other It is a topological concept – in other words, even if the circuit elements words, even if the circuit elements change values, the change values, the nodenode remains an remains an equipotential pointequipotential point. . To find a To find a nodenode, start at a point in the , start at a point in the circuit. From this point, everywhere you circuit. From this point, everywhere you can travel by moving only along perfect can travel by moving only along perfect conductors is part of a singleconductors is part of a single node node..


A A looploop is any closed path through a is any closed path through a circuit in which no node is encountered circuit in which no node is encountered more than once.more than once. To find a loop, start at a node in the To find a loop, start at a node in the circuit. From this node, travel along a circuit. From this node, travel along a path back to the same node ensuring that path back to the same node ensuring that you do not encounter any node more than you do not encounter any node more than once.once. A A meshmesh is a loop that has no other loops is a loop that has no other loops inside of it.inside of it.


If we know the voltage at every If we know the voltage at every node of a circuit relative to a node of a circuit relative to a reference node (reference node (groundground), then we ), then we know everything about the circuit know everything about the circuit – i.e., we can determine any other – i.e., we can determine any other voltage or current in the circuit.voltage or current in the circuit. The same is true if we know The same is true if we know every mesh current.every mesh current.

ResistorsResistors A resistor is a circuit element that A resistor is a circuit element that

dissipates electrical energy (usually as dissipates electrical energy (usually as heat).heat).

Real-world devices that are modeled by Real-world devices that are modeled by resistors: incandescent light bulb, resistors: incandescent light bulb, heating elements (stoves, heaters, etc.), heating elements (stoves, heaters, etc.), long wireslong wires

Parasitic resistances: many resistors on Parasitic resistances: many resistors on circuit diagrams model unwanted circuit diagrams model unwanted resistances in transistors, motors, etc.resistances in transistors, motors, etc.

ResistorsResistors

Resistance is measured in Ohms (Resistance is measured in Ohms ()) The relationship between terminal voltage The relationship between terminal voltage

and current is governed by and current is governed by Ohm’s lawOhm’s law Ohm’s law tells us that the volt drop in Ohm’s law tells us that the volt drop in

the direction of assumed current flow is the direction of assumed current flow is RiRi

The Rest of

the Circuit

R v(t)

i(t)+

-

tRitv

KCL and KVLKCL and KVL

Kirchhoff’s Current Law (Kirchhoff’s Current Law (KCLKCL) and ) and Kirchhoff’s Voltage Law (Kirchhoff’s Voltage Law (KVLKVL) are the ) are the fundamental laws of circuit analysis.fundamental laws of circuit analysis. KCLKCL is the basis of is the basis of nodal analysisnodal analysis – in – in which the unknowns are the voltages which the unknowns are the voltages at each of the at each of the nodesnodes of the circuit. of the circuit. KVLKVL is the basis of is the basis of mesh analysismesh analysis – in – in which the unknowns are the currents which the unknowns are the currents flowing in each of the flowing in each of the meshesmeshes of the of the circuit.circuit.


KCLKCL The sum of all The sum of all

currents entering currents entering a node is zero, ora node is zero, or

The sum of The sum of currents entering currents entering node is equal to node is equal to sum of currents sum of currents leaving node.leaving node.

i1(t)

i2(t) i4(t)

i5(t)

i3(t)

n

jj ti

1

0)(


KVLKVL The sum of The sum of

voltages around voltages around any loop in a any loop in a circuit is zero.circuit is zero.

0)(1

n

jj tv

+

-

v1(t)

+ +-

-

v2(t)

v3(t)


In KVL:In KVL: A voltage encountered + to - is positive.A voltage encountered + to - is positive. A voltage encountered - to + is A voltage encountered - to + is

negative.negative. Arrows are sometimes used to Arrows are sometimes used to

represent voltage differences; they represent voltage differences; they point from low to high voltage.point from low to high voltage.+

-

v(t) v(t)≡

Resistors in SeriesResistors in Series

A single loop circuit is one which A single loop circuit is one which has only a single loop.has only a single loop.

The same current flows through The same current flows through each element of the circuit - the each element of the circuit - the elements are in elements are in seriesseries. .


Two elements are in series if the Two elements are in series if the current that flows through one current that flows through one must also flow through the other.must also flow through the other.

R1 R2

Series


If we wish to replace the two If we wish to replace the two series resistors with a single series resistors with a single equivalentequivalent resistor whose voltage- resistor whose voltage-current relationship is the same, current relationship is the same, the the equivalentequivalent resistor has a value resistor has a value given bygiven by

21 RRReq

Resistors in SeriesResistors in Series For For NN resistors in series, the resistors in series, the equivalentequivalent resistor has a value given resistor has a value given byby

Neq RRRRR 321

R1

R3

R2 Req

Resistors in ParallelResistors in Parallel

When the terminals of two or When the terminals of two or more circuit elements are more circuit elements are connected to the same two connected to the same two nodes, the circuit elements are nodes, the circuit elements are said to be in said to be in parallelparallel. .

Resistors in ParallelResistors in Parallel

If we wish to replace the two If we wish to replace the two parallel resistors with a single parallel resistors with a single equivalentequivalent resistor whose voltage- resistor whose voltage-current relationship is the same, current relationship is the same, the the equivalentequivalent resistor has a value resistor has a value given bygiven by

21

21

RR

RRReq

Resistors in ParallelResistors in Parallel For For NN resistors in parallel, the resistors in parallel, the equivalentequivalent resistor has a value given resistor has a value given byby

N

eq

RRRR

R1111

1

321

ReqR3R2R1

Energy Storage ElementsEnergy Storage Elements

CapacitorsCapacitors store energy in an electric store energy in an electric field.field.

InductorsInductors store energy in a magnetic field. store energy in a magnetic field. Capacitors and inductors are passive Capacitors and inductors are passive

elements:elements: Can store energy supplied by circuitCan store energy supplied by circuit Can return stored energy to circuitCan return stored energy to circuit Cannot supply more energy to circuit than Cannot supply more energy to circuit than

is stored.is stored.

Energy Storage ElementsEnergy Storage Elements

Voltages and currents in a circuit Voltages and currents in a circuit withoutwithout energy storage elements energy storage elements are solutions to algebraic are solutions to algebraic equations.equations.

Voltages and currents in a circuit Voltages and currents in a circuit withwith energy storage elements are energy storage elements are solutions to linear, constant solutions to linear, constant coefficient differential equations.coefficient differential equations.


Capacitance occurs when two conductors Capacitance occurs when two conductors are separated by a dielectric (insulator).are separated by a dielectric (insulator).

Charge on the two conductors creates an Charge on the two conductors creates an electric field that stores energy.electric field that stores energy.

The voltage difference between the two The voltage difference between the two conductors is proportional to the charge.conductors is proportional to the charge.

The proportionality constant The proportionality constant CC is called is called capacitance.capacitance.

Capacitance is measured in Farads (F).Capacitance is measured in Farads (F).

tvCtq


The voltage across a capacitor The voltage across a capacitor cannot change instantaneously.cannot change instantaneously.

The energy stored in the The energy stored in the capacitors is given bycapacitors is given by

)(2

1)( 2 tCvtwC

InductorsInductors

Inductance occurs when current flows through Inductance occurs when current flows through a (real) conductor.a (real) conductor.

The current flowing through the conductor The current flowing through the conductor sets up a magnetic field that is proportional to sets up a magnetic field that is proportional to the current.the current.

The voltage difference across the conductor is The voltage difference across the conductor is proportional to the rate of change of the proportional to the rate of change of the magnetic flux.magnetic flux.

The proportionality constant is called the The proportionality constant is called the inductance, denoted inductance, denoted L.L.

Inductance is measured in Henrys (H).Inductance is measured in Henrys (H).

Documents

ARRDEKTA INSTITUTE OF TECHNOLOGY GUIDED BY. GUIDED BY. Prof.Y.B.Vaghela. Prof.Y.B.Vaghela. Asst.prof in electrical Asst.prof in electrical Department Department