ARRDEKTA INSTITUTE OF ARRDEKTA INSTITUTE OF TECHNOLOGYTECHNOLOGY

GUIDED BYGUIDED BY Prof. R.H.Chaudhary Prof. R.H.Chaudhary

Asst.prof in electricalAsst.prof in electrical

Department Department

PREPARED BYPREPARED BY Rajpurohit Anurag Rajpurohit Anurag

(130930107011)(130930107011) Soneri Sahil Soneri Sahil

(130930107014)(130930107014) Vaghasiya Chirag Vaghasiya Chirag

(130930107015)(130930107015) Bhati Sejal Bhati Sejal

(130930107001)(130930107001)

An AC circuit consists of a combination An AC circuit consists of a combination of circuit elements and an AC generator of circuit elements and an AC generator or sourceor source

The output of an AC generator is The output of an AC generator is sinusoidal and varies with time sinusoidal and varies with time according to the following equationaccording to the following equation Δv = ΔVΔv = ΔVmaxmax sin 2 sin 2ƒtƒt

Δv is the instantaneous voltageΔv is the instantaneous voltage ΔVΔVmaxmax is the maximum voltage of the generator is the maximum voltage of the generator ƒ is the frequency at which the voltage changes, ƒ is the frequency at which the voltage changes,

in Hzin Hz

AC Circuit AC Circuit

Resistor in an AC CircuitResistor in an AC Circuit Consider a circuit Consider a circuit

consisting of an AC consisting of an AC source and a resistorsource and a resistor

The graph shows the The graph shows the current through and the current through and the voltage across the voltage across the resistorresistor

The current and the The current and the voltage reach their voltage reach their maximum values at the maximum values at the same timesame time

The current and the The current and the voltage are said to be voltage are said to be in in phasephase

More About Resistors in an More About Resistors in an AC CircuitAC Circuit

The direction of the current has no effect The direction of the current has no effect on the behavior of the resistoron the behavior of the resistor

The rate at which electrical energy is The rate at which electrical energy is dissipated in the circuit is given bydissipated in the circuit is given by P = iP = i22 R R

where i is the where i is the instantaneous currentinstantaneous current the heating effect produced by an AC current with a the heating effect produced by an AC current with a

maximum value of Imaximum value of Imaxmax is not the same as that of a is not the same as that of a DC current of the same valueDC current of the same value

The maximum current occurs for a small amount of The maximum current occurs for a small amount of timetime

rms Current and Voltagerms Current and Voltage

The The rms currentrms current is the direct is the direct current that would dissipate the current that would dissipate the same amount of energy in a same amount of energy in a resistor as is actually dissipated by resistor as is actually dissipated by the AC currentthe AC current

Alternating voltages can also be Alternating voltages can also be discussed in terms of rms valuesdiscussed in terms of rms values

maxmax

rms I707.02

II

maxmax

rms V707.02

VV

Ohm’s Law in an AC Ohm’s Law in an AC CircuitCircuit

rms values will be used when rms values will be used when discussing AC currents and voltagesdiscussing AC currents and voltages AC ammeters and voltmeters are AC ammeters and voltmeters are

designed to read rms valuesdesigned to read rms values Many of the equations will be in the Many of the equations will be in the

same form as in DC circuitssame form as in DC circuits Ohm’s Law for a resistor, R, in an Ohm’s Law for a resistor, R, in an

AC circuitAC circuit ΔVΔVrmsrms = I = Irmsrms R R

Also applies to the maximum values of v Also applies to the maximum values of v and iand i

Capacitors in an AC CircuitCapacitors in an AC Circuit

Consider a circuit containing a capacitor Consider a circuit containing a capacitor and an AC sourceand an AC source

The current starts out at a large value and The current starts out at a large value and charges the plates of the capacitorcharges the plates of the capacitor There is initially no resistance to hinder the flow There is initially no resistance to hinder the flow

of the current while the plates are not chargedof the current while the plates are not charged As the charge on the plates increases, the As the charge on the plates increases, the

voltage across the plates increases and the voltage across the plates increases and the current flowing in the circuit decreasescurrent flowing in the circuit decreases

More About Capacitors in More About Capacitors in an AC Circuitan AC Circuit

The current The current reverses directionreverses direction

The voltage across The voltage across the plates the plates decreases as the decreases as the plates lose the plates lose the charge they had charge they had accumulatedaccumulated

The voltage across The voltage across the capacitor lags the capacitor lags behind the current behind the current by 90°by 90°

Capacitive Reactance and Capacitive Reactance and Ohm’s LawOhm’s Law

The impeding effect of a capacitor on the The impeding effect of a capacitor on the current in an AC circuit is called the current in an AC circuit is called the capacitive reactancecapacitive reactance and is given by and is given by

When ƒ is in Hz and C is in F, XWhen ƒ is in Hz and C is in F, XCC will be in will be in ohmsohms

Ohm’s Law for a capacitor in an AC circuitOhm’s Law for a capacitor in an AC circuit ΔVΔVrmsrms = I = Irmsrms X XCC

Cƒ2

1XC

Inductors in an AC CircuitInductors in an AC Circuit

Consider an AC Consider an AC circuit with a source circuit with a source and an inductorand an inductor

The current in the The current in the circuit is impeded by circuit is impeded by the back emf of the the back emf of the inductorinductor

The voltage across The voltage across the inductor always the inductor always leads the current by leads the current by 90°90°

Inductive Reactance and Inductive Reactance and Ohm’s LawOhm’s Law

The effective resistance of a coil in The effective resistance of a coil in an AC circuit is called its an AC circuit is called its inductive inductive reactancereactance and is given by and is given by XXLL = 2 = 2ƒLƒL

When ƒ is in Hz and L is in H, XWhen ƒ is in Hz and L is in H, XLL will be in will be in ohmsohms

Ohm’s Law for the inductorOhm’s Law for the inductor ΔVΔVrmsrms = I = Irmsrms X XLL

The RLC Series CircuitThe RLC Series Circuit

The resistor, The resistor, inductor, and inductor, and capacitor can be capacitor can be combined in a combined in a circuitcircuit

The current in the The current in the circuit is the same circuit is the same at any time and at any time and varies sinusoidally varies sinusoidally with timewith time

Current and Voltage Current and Voltage Relationships in an RLC Relationships in an RLC CircuitCircuit

The instantaneous The instantaneous voltage across the voltage across the resistor is in phase resistor is in phase with the currentwith the current

The instantaneous The instantaneous voltage across the voltage across the inductor leads the inductor leads the current by 90°current by 90°

The instantaneous The instantaneous voltage across the voltage across the capacitor lags the capacitor lags the current by 90°current by 90°

Phasor DiagramsPhasor Diagrams To account for the To account for the

different phases of the different phases of the voltage drops, vector voltage drops, vector techniques are usedtechniques are used

Represent the voltage Represent the voltage across each element across each element as a rotating vector, as a rotating vector, called a called a phasorphasor

The diagram is called The diagram is called a a phasor diagramphasor diagram

Phasor Diagram for RLC Phasor Diagram for RLC Series CircuitSeries Circuit

The voltage across the The voltage across the resistor is on the +x resistor is on the +x axis since it is in phase axis since it is in phase with the currentwith the current

The voltage across the The voltage across the inductor is on the +y inductor is on the +y since it leads the since it leads the current by 90°current by 90°

The voltage across the The voltage across the capacitor is on the –y capacitor is on the –y axis since it lags axis since it lags behind the current by behind the current by 90°90°

Phasor Diagram, contPhasor Diagram, cont

The phasors are The phasors are added as vectors to added as vectors to account for the account for the phase differences in phase differences in the voltagesthe voltages

ΔVΔVLL and ΔV and ΔVCC are on are on the same line and the same line and so the net y so the net y component is ΔVcomponent is ΔVL L - - ΔVΔVCC

ΔVΔVmaxmax From the Phasor From the Phasor DiagramDiagram

The voltages are not in phase, so they The voltages are not in phase, so they cannot simply be added to get the cannot simply be added to get the voltage across the combination of the voltage across the combination of the elements or the voltage sourceelements or the voltage source

is the is the phase anglephase angle between the between the current and the maximum voltagecurrent and the maximum voltage

R

CL

2CL

2Rmax

V

VVtan

)VV(VV

Impedance of a CircuitImpedance of a Circuit

The impedance, The impedance, Z, can also be Z, can also be represented in a represented in a phasor diagramphasor diagram

R

XXtan

)XX(RZ

CL

2CL

2

Impedance and Ohm’s Impedance and Ohm’s LawLaw

Ohm’s Law can be applied to the Ohm’s Law can be applied to the impedanceimpedance ΔVΔVmaxmax = I = Imaxmax Z Z

Summary of Circuit Summary of Circuit Elements, Impedance and Elements, Impedance and Phase AnglesPhase Angles

Problem Solving for AC Problem Solving for AC CircuitsCircuits

Calculate as many unknown Calculate as many unknown quantities as possiblequantities as possible For example, find XFor example, find XLL and X and XCC

Be careful of units -- use F, H, Be careful of units -- use F, H, ΩΩ Apply Ohm’s Law to the portion of Apply Ohm’s Law to the portion of

the circuit that is of interestthe circuit that is of interest Determine all the unknowns asked Determine all the unknowns asked

for in the problemfor in the problem

Power in an AC Circuit, Power in an AC Circuit, contcont

The average power delivered by The average power delivered by the generator is converted to the generator is converted to internal energy in the resistorinternal energy in the resistor PPavav = I = IrmsrmsΔVΔVRR = = IIrmsrmsΔVΔVrmsrms cos cos cos cos is called the is called the power factorpower factor of the of the

circuitcircuit Phase shifts can be used to Phase shifts can be used to

maximize power outputsmaximize power outputs

Maxwell’s Starting PointsMaxwell’s Starting Points

Electric field lines originate on positive Electric field lines originate on positive charges and terminate on negative chargescharges and terminate on negative charges

Magnetic field lines always form closed loops Magnetic field lines always form closed loops – they do not begin or end anywhere– they do not begin or end anywhere

A varying magnetic field induces an emf and A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)hence an electric field (Faraday’s Law)

Magnetic fields are generated by moving Magnetic fields are generated by moving charges or currents (Ampcharges or currents (Ampère’s Law)ère’s Law)

Hertz’s Basic LC CircuitHertz’s Basic LC Circuit When the switch is When the switch is

closed, oscillations closed, oscillations occur in the current occur in the current and in the charge on and in the charge on the capacitorthe capacitor

When the capacitor is When the capacitor is fully charged, the total fully charged, the total energy of the circuit is energy of the circuit is stored in the electric stored in the electric field of the capacitorfield of the capacitor At this time, the current At this time, the current

is zero and no energy is is zero and no energy is stored in the inductorstored in the inductor

LC Circuit, contLC Circuit, cont As the capacitor discharges, the energy stored As the capacitor discharges, the energy stored

in the electric field decreasesin the electric field decreases At the same time, the current increases and the At the same time, the current increases and the

energy stored in the magnetic field increasesenergy stored in the magnetic field increases When the capacitor is fully discharged, there is When the capacitor is fully discharged, there is

no energy stored in its electric fieldno energy stored in its electric field The current is at a maximum and all the energy The current is at a maximum and all the energy

is stored in the magnetic field in the inductoris stored in the magnetic field in the inductor The process repeats in the opposite directionThe process repeats in the opposite direction There is a continuous transfer of energy There is a continuous transfer of energy

between the inductor and the capacitorbetween the inductor and the capacitor

Electromagnetic Waves Electromagnetic Waves are Transverse Wavesare Transverse Waves

TheThe E E and and BB fields fields are perpendicular are perpendicular to each otherto each other

Both fields are Both fields are perpendicular to perpendicular to the direction of the direction of motionmotion Therefore, em Therefore, em

waves are waves are transverse wavestransverse waves