# What is Complex power: Definition and 41 Discussions

Instantaneous power in an electric circuit is the rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductors and capacitors may result in periodic reversals of the direction of energy flow.
The portion of instantaneous power that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as instantaneous active power, and its time average is known as active power or real power. The portion of instantaneous power that results in no net transfer of energy but instead oscillates between the source and load in each cycle due to stored energy, is known as instantaneous reactive power, and its amplitude is the absolute value of reactive power.

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1. ### Question about complex power in three phase circuits

Homework Statement Assume that the two balanced loads are supplied by an 840-V rms 60-Hz line. Load #1: Y-connected with 30+j40 Ω per phase, Load #2: balanced three-phase motor drawing 48 kW at a power factor of 0.8 lagging. Assuming abc sequence, calculate the complex power absorbed by the...
2. ### Working with phasors (Circuits, such as complex power)

Homework Statement I am going over examples in my textbook and I came across this: I don't understand how they converted 18.265 at angle of 39.9 to 14.02+j11.71 Homework Equations I know how to convert from the imaginary numbers into the angle form, usually I use: Is there another equation...
3. ### Complex Power Homework: Is My Solution Right?

Homework Statement y = 27 Homework Equations The Attempt at a Solution - I calculated the total impedance. - Divide it with the voltage to get the current. - Then I use the load impedance to find the voltage load. - And I calculated the complex power for the load. I am not comfortable...
4. ### Apparent Power vs Complex Power: Understand the Difference

What is the difference between apparent power and complex power? How to differentiate them?
5. ### Supplied complex power from source vs consumed by load

Homework Statement Homework Equations S= 3VaIa* The Attempt at a Solution After transformation: Ia = 120<0 / (6+8j) = 12<-53.13 A Total complex power = 3 * Va * Ia* = 3*120<0 * 12<53.13 = 2592W + j3456 VAR This is the power supplied from source. What would be the power consumed by load?
6. ### Verifying Complex Power Calculations

Homework Statement Calculate the complex power delivered by the source V = 12cos(wt) V Homework Equations V = IR The Attempt at a Solution 1. I combined 8ohm resistor and 8j ohm inductor in parallel to get 4+4j ohms 2. I combined that with 4ohm resistor in series to get a Zth of 8+4j ohms 3...
7. ### Finding complex power in AC circuit

In a branch I have to find complex power which is having current 19.41<-37.3 A and impedance 4+j3 Ω What I used is i2z and I was getting 1489.85 - j1152.74 W. This is wrong but I don't know how because by this site the answer was different...
8. ### MHB Uniform convergence of a complex power series on a compact set

I need to prove that the complex power series $\sum\limits_{n=0}^{\infty}a_nz^n$ converges uniformly on the compact disc $|z| \leq r|z_0|,$ assuming that the series converges for some $z_0 \neq 0.$ *I know that the series converges absolutely for every $z,$ such that $|z|<|z_0|.$ Since...
9. ### Complex Power Q: Solved w/ My Friend & I

Homework Statement [moderator note: Image inserted to be visible in problem statement] Homework EquationsThe Attempt at a Solution My friend and I are trying to figure out how this works. This is the questions and the solution manual. We understand where the real power comes from but not at...
10. ### Differentiate x to a complex power?

Is it possible to differentiate xa+bi where a and b are real ? if so what is the answer ?
11. ### Understanding Reactive Power and Reactance: Exploring Complex Power Components

Complex power has two components the "active" and the "reactive". I am comfused. What is the physical interpretation of the complex component? Also what is the reactance?
12. ### Complex power question. What is S exactly?

I know that S = P +jQ however I am kind of unsure of what S exactly is. Is S the power supplied to the circuit of which only P is used by a load (e.g. powering a light bulb) whilst the Q component is wasted? Thanks
13. ### Exploring the Relationship Between Complex Power and RL and RC Circuits

Is this true? Or is this true? Ø and Q are from this equation:
14. ### Network, 2 loads, find complex power

Homework Statement http://imageshack.us/a/img819/9791/sh5k.jpg Given the network [above], find the complex power supplied by the source, the power factor of the source, and the voltage Vs(t). The frequency is 60 Hz. Homework Equations ω=1/f Pf = cosø P = IV PL =...
15. ### Radius of convergance complex power series

Homework Statement https://scontent-a.xx.fbcdn.net/hphotos-ash3/1390611_10201748262844961_2141774184_n.jpg I need help with 7b. Theorem 3 = termwise differentiation and theorem 4 = termwise integration.Homework Equations The Attempt at a Solution I have no idea how differentiation or...
16. ### Complex Power with power factor

By definition,Ia=(S/3V)* I want to know if there is power factor, say cosϕ=0.8 Should Ia=(S/(3V*0.8)) or just Ia =(S/3V)*? Because in the reference book, it sometimes consider the power factor but sometimes don't, I am quite confused with it.
17. ### Is this the right way to find impedance using complex power and volta

Homework Statement The load (Z) in the circuit below absorbs a complex power of 54+j46 VA when the voltage across it is 3cos(400t+-60)V. Use this information to determine the impedance of the loadHomework Equations P = V^2 / Z The Attempt at a Solution first convert V to polar form 3 <...
18. ### Capacitance with complex power connected to voltage, AC.

So I'm trying to solve this kind of problem And I got stuck. Capacitor with power 2000*e^(-jPi/2) and connected to voltage u(t)=282,84sin(314*t+Pi/4). Determine the capacity. I know power is P=U*I, capacitance is C = 1 / Xc*w, from that u(t) we have that w is 314, so rearraning equation P =...
19. ### Simple complex power: why is e^( i (2*Pi*n*t)/T ) not 1?

the complex form of Fourier series is: f(t) = Ʃ c*e^[iωnt] where c are the coefficients, the sum is from n= -inf to +inf; ω= 2*pi/T, where T is period... but if you just look at e^[iωnt] = e^[ i (2*pi*n*t)/T] = {e^[ i (2*pi*n)] }^(t/T) where I just took out the t/T... well, e^[ i...
20. ### Complex Power, calc load impedance

Homework Statement A load absorbs 58959W at a lagging power factor of pf = 0.73. If the current flowing through the load is ix = 0.001A-rms , determine the impedance of the load. Homework Equations Ohms law Impedance/Voltage/Power Triangles The Attempt at a Solution If the load...
21. ### Sinusoidal sources and complex power

When calculating power in a given circuit, why is the complex conjugate of the current used to compute power?
22. ### Solving Complex Power with a 400-V, 100-Hz Source and a Load of 400+j30 VA

Homework Statement 1. A 400-V, 100-Hz source supplies power to a load. If the load absorbs 400+j30 VA of power, find the following: (2 pts each) a. The magnitude of current drawn by the load. b. The apparent power absorbed by the load. c. The power factor of the load. d. The impedance of...
23. ### Complex power raised over real number.

1. I actually don't know if such kind of operation is even allowed. A friend of mine raised this question, that can we raise a complex power over a real number. I solved it this way. Is this correct? http://i45.tinypic.com/254vwux.jpg Homework Statement Homework Equations The Attempt at a...
24. ### Taking e to a complex power (telecommunication formula)

Hello, I am have this telecommunications formula which calculates the magnitude of a wave on a transmission line: VO = VI e^(-yi) where: VO = voltage out. VI = voltage in (5) y = propagation coefficient (0.745 + j1.279) i = length of line (2500) I am trying to use it to calculate the...
25. ### Complex Power Series Radius of Convergence Proof

Homework Statement If f(z) = \sum an(z-z0)n has radius of convergence R > 0 and if f(z) = 0 for all z, |z - z0| < r ≤ R, show that a0 = a1 = ... = 0. Homework Equations The Attempt at a Solution I know it is a power series and because R is positive I know it converges. And if...
26. ### Complex Power Series Convergence Help

Homework Statement I have a problem set that asks me to determine, first, the radius of convergence of a complex series (using the limit of the coefficients), and second, whether or not the series converges anywhere on the radius of convergence. Homework Equations As an example: Σ(z+3)k2 with...
27. ### Converting complex power series into a function

Hey guys, sorry for sending out so many questions so fast. I just discovered this site, and it looks great. Plus, I have my first complex analysis midterm tomorrow, so I'm pretty stressed (you'd think after 4 years of math/econ/computer science you'd get used to it but there's nothing like the...
28. ### Can someone explain the resolution to the complex power paradox?

Hi, Can anyone help me resolve and understand this paradox: e=e^{1+2i\pi} and so e=\left[e^{1+2\pi i}\right]^{1+2\pi i}=e^{1+4\pi i-4\pi^2}=e^{1-4\pi^2} which is obviously fallacious. This paradox is from Roger Penrose Road to Reality and is currently hurting my head. I keep...
29. ### Engineering Calculating Average and Reactive Power in Complex Circuits

[b]1. Homework Statement [/ 1) Find the average and relative power for the voltage source and for each impedance branch. Are they absorbing or delivering average power/magnetizing VARS? Homework Equations Those derived and average power=P=((Vm*Im)/2)*(cos(theta(v)-theta(i)) reactive...
30. ### Understanding Complex Power Calculations: Why is S = 1/2 * V * I?

I don't have a question about a specific HW problem, just a general questions. When calculating complex power, I understand it's S = Veff*Ieff(conjugate). However, S can also be calculate as S = 1/2 * V * I. Why is this? I feel I'm missing something simple, but I'm pretty lost because...
31. ### Engineering Circuits (Power and Complex Power) Help

Homework Statement Homework Equations The Attempt at a Solution I am just lost on these two problems. What I think on the first one is that I have to convert the voltage but from there I am lost. I am guessing I also have to figure the current. For the second problem, I know that S = P + Q. I...
32. ### Why do we need to take the conjugate in complex power calculations?

Ive seen in some situations the equation S=VI is being used with the conjugate of I IN what situations do you have to take the conjugate and why?
33. ### Calculating Complex Power: P+jQ

power=P+P(cos(2wt))+Q(cos(2wt)) but complex power = P+jQ am i to assume that complex power is a phasor representation of the last two terms? why does this formula ignore the first term?
34. ### Complex power series question

Homework Statement Suppose that f(z) = ∑a_j.z^j for all complex z, the sum goes from j=0 to infinity. (a) Find the power series expansion for f' (b) Where does it converge? (c) Find the power series expansion for f^2 (d) Where does it converge? (e) Suppose that f'(x)^2 + f(x)^2 = 1...
35. ### Differentiating a complex power series

Homework Statement Say f(z) = Σ(z^n), with sum from 0 to infinity Then we can say f'(z) = Σn(z^n-1), with sum from 0 to infinity (i) = Σn(z^n-1), with sum from 1 to infinity (as the zero-th term is 0)...
36. ### Division of complex power series

Homework Statement Find tan(z) up to the z^7 term, where tan(z) = sin(z)/cos(z) Homework Equations sin(z) = z - z^3/3! + z^5/5! - z^7/7! + ... cos(z) = 1 - z^2/2! + z^4/4! - z^6/6! + ... The Attempt at a Solution Hi, Seeing as sin and cos have the same power series as for when...
37. ### Finding b_k in a Complex Power Series

Homework Statement There is a power series \infty \sumb_k.z^k n=0 such that \infty (exp(z) - 1)\sumb_k.z^k = z n=0 the infinity and n=0 are meant to be over the sigma, sorry Find b_k for k...
38. ### Radius of convergence of complex power series

Homework Statement Find the radius of convergence of the series: ∞ ∑ n^-1.z^n n=1 Use the following lemma: ∞ ∞ If |z_1 - w| < |z_2 - w| and if ∑a_n.(z_2 - w)^n converges, then ∑a_n.(z_1 - w)^n also...
39. ### Complex power calculations formula

I'm confused about a point concerning complex power calculations. The formula my text gives is S=V(eff)I(eff)*. I'm confused about what the conjugate is for I(eff). The way I understand it, I(eff) = I(rms) and I(rms) = I(m)/√2. Since I(m) is a real number, and I(m)/√2 is real, how is there a...
40. ### Complex Power Series: Does Absolute Convergence Imply Convergence?

Homework Statement Hi all. In my book on complex analysis, they discuss complex power series. They use a variety of "tests" to determine absolute convergence, but they never say if this also implies convergence. Does it? Niles.
41. ### Complex power series to calculate Fourier series

I never took complex analysis in undergrad and always regretted it, so I'm working through the book Visual Complex Analysis on my own. Really enjoying it so far. Homework Statement Actually you can view the problem...