POWER IN AC CIRCUITBY

Group

GROUP

MUHAMMAD UMER FAROOQ BS-P-13-28

MUHAMMAD FAISAL KHAN BS-P-13-57

MUHAMMAD AKHTAR BS-P-13-31

MUHAMMAD USMAN NAJEEB BS-P-13-67

Power

Mechanics

rate of doing work per unit time

P=W/t

CIRCUIT

The work done dW by a source of emf to unit charge dq is given by

dW=Ɛ dq

the rate of doing work by source of emf to unit charge in unit time

called power. P=dW/dt

POWERA.C

P=

=R/2

=

=cos

D.C P=VI

P=R

P=/R

Cases

IDEAL case

ideal capacitive and inductive elements have no internal resistance.

so power will go on resistive element and then it is given by

P=t-

full A.C circuit

sint sin(t-)

=

DERIVATIONS

P=t-

=R/2

=

since /2)

=R

In RLC circuit

P=t- sin

P=t cos- sin

P=t cos-

The t term gives the value ½.,wheras the term gives ‘0’

So we can write it as

=cos/2 /

=cos /2

Power factor

=cos

in this, cos is called power factor. Power factor for series RLC circuit. tan we can show that

cos

the power delivered to the circuit by the source of emf is maximum when cos.when circuit is purely resistive, no capacitor or inductor , or at resonance when so that Z=R. then average power is

=

Phase angle

an angle representing a difference in phase, 360 degrees (2π radians) corresponding to one complete cycle.

The angle between two alternating quantities

PHASOR DIAGRAM

the diagram in which phasors represented by the open arrows, rotate counterclockwise with an angular frequency about the origin.

Properties of phasor diagram

The length of phasors

proportional to max. value of alternating quantity

Projection of phasor on a vertical axis

instantaneous value of alternating quantity

arrows on vertical axis represent the time varying quantities

Phase Angles

resistance circuit

waveform phasor daigram

𝑉 𝑅

𝐼𝑅t

𝜔

Capacitor circuit

Inductor circuit

𝑉 𝐿

𝐼𝐿

90𝑜

𝜔

RLC circuit

Power companies

frequency 60Hz

Not concerned

whether you use purely resistive device in which power dissipated in phase

with the source of emf

or

partialy capacitive or inductive device.

as motor

Power companies measurement

Two cases

1. if the power companies measured your energy use in a time smaller than 1/60 s they would notice variations in the rate at which you use energy.

2. measuring over a time longer than 1/60 s only the average rate of energy consumption becomes important.

Question & Answer

SPECIAL THANKS

DR. FAYYAZ HUSSAIN

THANKS

GROUP MEMBERS

THANKS

BY

GROUP MEMBERS