For the following voltage and current phasors, calculate the...

For the following voltage and current phasors, calculate the complex power, apparent power, real power, and reactive power. Specify whether the pf is leading or lagging. (a) $\mathbf{V}=220 / 30^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{I}=0.5 / 60^{\circ} \mathrm{Arms}$ (b) $\mathbf{V}=250 \angle-10^{\circ} \mathrm{Vrms}$ $\mathbf{I}=6.2 \angle-25^{\circ} \mathrm{A} \mathrm{rms}$ (c) $\mathbf{V}=120 / 0^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{I}=2.4 /-15^{\circ} \mathrm{Arms}$ (d) $\mathbf{V}=160 / 45^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{I}=8.5 / 90^{\circ} \mathrm{Arms}$

For the following voltage and current phasors, calculate the complex power, apparent power, real power, and reactive power. Specify whether the pf is leading or lagging.
(a) $\mathbf{V}=220 / 30^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{I}=0.5 / 60^{\circ} \mathrm{Arms}$
(b) $\mathbf{V}=250 \angle-10^{\circ} \mathrm{Vrms}$
$\mathbf{I}=6.2 \angle-25^{\circ} \mathrm{A} \mathrm{rms}$
(c) $\mathbf{V}=120 / 0^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{I}=2.4 /-15^{\circ} \mathrm{Arms}$
(d) $\mathbf{V}=160 / 45^{\circ} \mathrm{V} \mathrm{rms}, \mathbf{I}=8.5 / 90^{\circ} \mathrm{Arms}$

Key Concepts

Real Power

Real power, also known as active power, is the component of complex power that performs actual work or generates heat. It is measured in watts (W) and is calculated using the product of the voltage, the current, and the cosine of the phase angle between them.

Apparent Power

Apparent power is the magnitude of the complex power and is measured in volt-amperes (VA). It represents the total power flowing in the circuit, combining both real power and reactive power, and provides an indication of the capacity of the electrical equipment without distinguishing how much power is actually converted to work.

Reactive Power

Reactive power is the component of complex power associated with energy storage and release in the reactive elements of a circuit, such as inductors and capacitors. Measured in volt-amperes reactive (VAR), it represents power that oscillates between the source and the load, rather than being consumed.

Phasor Representation

Phasors are a method of representing sinusoidally varying quantities as complex numbers or rotating vectors in the complex plane. This representation simplifies the analysis of AC circuits by allowing the use of algebraic operations to handle phase differences and magnitudes rather than solving differential equations directly.

Complex Power

Complex power is a comprehensive representation of power in AC circuits, expressed as a complex number that consists of both real (active) power and reactive power components. It is typically calculated by taking the product of the voltage phasor and the complex conjugate of the current phasor, encapsulating both energy consumption and exchange effects.

Power Factor

The power factor measures the efficiency with which an AC circuit consumes power and is defined as the ratio of real power to apparent power. It is closely related to the phase angle between the voltage and current, with a lagging power factor indicating an inductive load and a leading power factor indicating a capacitive load. A power factor close to one signifies efficient power usage.

Transcript

00:01 For the following voltage and current phasers calculate the complex power, apparent power, real power and reactive power, and specify whether the power factor is leading or lagging.

00:30 The first is v equals 220 angle 30 degree v rms and i is 0 .5 angle 60 degree a rmsmns b is v equals 250 minus 10 degree v rms and i is 6 .2 angle minus 25 degree a rmsms c is v equals 120 degree v rm s and i is 2 .4 minus 15 degrees a rms.

01:14 For d v equals 160 45 degree vrms and i equals 8 .5 angle 90 degree a rmsmns now for the first part, voltage is equal to vrms angle theta v which is equal to 220 angle 30 degree and i is i rms angle theta i which is equal to 0 .5 angle 60 degree.

01:57 Now determining the complex power s equals vrms into the conjugate of irms which is equal to irms which is equal to to 220 angle 30 .5 angle 60 which is equals to 1110 angle 30 degree volt ampere in the converted form it will be 95 .26 minus j 55 volt ampere this is the complex power now finding the apparent power which is the mod of s that is magnitude so magnitude of vrms, multiple magnitude of irms, which is equal to 220 into 0 .5, that is 110 volt ampere.

02:54 Now finding the real power is the real value of s, which is equals to s cos, theta v minus theta i.

03:05 This is equal to 110 cost 30 degree minus 60 degree, that is equal to 95 .0.

03:12 26 what determining the reactive power the reactive power is given by the imaginary portion of the s which is s sign theta v minus theta i that is equals to 1110 sign 30 degree minus 60 degree which is equals to minus 55 ompra r this is the reactive power now determining the power factor is cause of theta v minus theta i that is equals to cost of minus 30 degrees is 0 .8 6 and it means that it is leading now going on to the second part where the complex v is 250 angle minus 18 and i equals 6 .2 angle minus 25 degree 8.

04:22 Here the complex power can be written as equals vrms into the conjugate value of i, which is 250 angle minus 10, 6 .2 angle minus 25 degree.

04:43 The conjugate of it will be the positive one that is equals to 15 degree volt ampere.

04:52 This is the complex power...

Please give Ace some feedback