Show power and power factor in ac circuits, Electrical Engineering

Assignment Help:

Q. Show Power and Power Factor in ac Circuits?

Power is the rate of change of energy with respect to time. The unit of power is a watt (W), which is a joule per second (J/s). The use of rms or effective values of voltage and current allows the average power to be found from phasor quantities. Let us consider a circuit consisting of an impedance Z φ = R + jX excited by an applied voltage of v(t) = √2 Vrmscos (ωt + φ), producing a current of i(t) =√2 Irmscosωt . The corresponding voltage and current phasors are then given by V φ and I0°, which satisfy the Ohm's-law relation ¯ V/ ¯ I = V φ/I 0° = Z φ.

The instantaneous power p(t) supplied to the network by the source is

1343_Show Power and Power Factor in ac Circuits.png

which can be rearranged as follows by using trigonometric relations:

2034_Show Power and Power Factor in ac Circuits1.png

Atypical plot of p(t) is shown in Figure, revealing that it is the sumof an average component, VrmsIrms cos φ, which is a constant that is time independent, and a sinusoidal component, VrmsIrms cos(2ωt +φ), which oscillates at a frequency double that of the original source frequency and has zero average value. The average component represents the electric power delivered to the circuit, whereas the sinusoidal component reveals that the energy is stored over one part of the period and released over another, thereby denoting no net delivery of electric energy. It can be seen that the power p(t) is pulsating in time and its time-average value P is given by Pav = Vrms Irms cos φ since the time-average values of the terms cos 2ωt and sin 2ωt are zero. Note that φ is the angle associated with the impedance, and is also the phase angle between the voltage and the current.

The term cos φ is called the power factor. An inductive circuit, in which the current lags the voltage, is said to have a lagging power factor, whereas a capacitive circuit, in which the current leads the voltage, is said to have a leading power factor. Notice that the power factor associated with a purely resistive load is unity, whereas that of a purely inductive load is zero (lagging) and that of a purely capacitive load is zero (leading).


Related Discussions:- Show power and power factor in ac circuits

Briefly explain about laplace transform, Q. Briefly explain about Laplace t...

Q. Briefly explain about Laplace transform? Many commonly encountered excitations can be represented by exponential functions. The differential equations describing the network

Subtract contents of memory and borrow from accumulator, Subtract Contents ...

Subtract Contents of Memory and Borrow from Accumulator The contents of the  memory  pointed  by the HL register  pair  and the borrow  flag are subtracted from the  contents

SINGLE-PHASE INDUCTION MOTORS MOTORS, HOW DOES SINGLE PHASE INDUCTION MOTOR...

HOW DOES SINGLE PHASE INDUCTION MOTORS DEVELOP A STARTING TORQUE ?

Electrical System Design, List four sources of information which are essent...

List four sources of information which are essential to the designer of this electrical installation

Circuit theory, Use basic circuit theory to convert the "T" circuit be...

Use basic circuit theory to convert the "T" circuit below into the equivalent "π". Hint: Remember to disconnect the voltage source and the load.

Short note on types of enclosure of machine, Q.   Write a short note on typ...

Q.   Write a short note on types of enclosure of machine. Sol.       The various types of d.c. machine :              (1) Magnetic frame or Yoke              (2)

Where does cpu enhanced mode originate from, Intel's 80386 was the first 32...

Intel's 80386 was the first 32-bit processor, and as the company had to backward-support the 8086. All the modern Intel-based processors run in the improved mode, capable of switch

Explain bandwidth and applications of rc coupled amplifier, Q. Explain the ...

Q. Explain the bandwidth for the curve and the applications of an RC coupled amplifier. Frequency response curve of an RC coupled amplifier was shown above(prev page). The cut

Explain the effect of a dielectric on behaviour of capacitor, Explain the e...

Explain the effect of a dielectric on the behaviour of a capacitor. If two parallel plates are separated by a distance 'd' (meters) in vacuum and are kept at a potential diffe

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd