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Why does phasor multiplication produce a different result with actual sine multiplication?

I thought phasors were shortcuts to the Euler's formula when dealing with sine functions. For example, $$\begin{align}\cos(t+a)+\cos(t+b)&=Re\{e^{j(t+a)}+e^{j(t+b)}\}\\ &=Re\{e^{jt}[(\cos a + \...
xiver77's user avatar
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1 answer
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AC Phasor Angles in Complex Number Analysis

I'm not sure if this problem is unique to me, but it's been breaking my brain for the past few months. While assuming phasor angles for AC circuit analysis using complex numbers, my teacher said that ...
RIKIPONDI's user avatar
0 votes
1 answer
97 views

When can we apply phasor analysis to an \$RLC\$ circuit?

This answer of mine shows that not every \$RLC\$ circuit reaches sinusoidal steady state at input frequency. A well-known theorem states that: If all natural frequencies of a uniquely solvable LTI ...
Sgg8's user avatar
  • 163
2 votes
4 answers
861 views

How can I mathematically show that multiplication of j will cause a phase shift?

I have a simple question that I cannot seem to wrap my head around. let's say I have a function Asin(wt), if I multiply a '-j' by this function to get: -jAsin(w*t), I have been told that this is ...
Josh Girgis's user avatar
0 votes
4 answers
154 views

AC Circuit Analysis - Mesh Analysis With Unknown Impedance Value

I attempted the problem below using mesh analysis, but I'm struggling to figure out how to solve and find the impedance Z. I feel like I'm forgetting something very basic, but I can't figure out what ...
Sam Fuller's user avatar
1 vote
1 answer
91 views

Why is clockwise KVL done like this?

My task is to find voltage across the resistor of this circuit where all the 4 components are connected in series with each other. The given information are : V1 (t) = 100 * sin(100 * t) V, R = 100 ...
RK Eshat's user avatar
  • 153
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1 answer
137 views

Finding the voltage across the resistor and the phase angle for Vs [closed]

I used KVL to find the voltage across the resistor but how could I solve this if the phasor angle Vs is unknown? So far I only got the solution up until the equation for KVL which is $$ V_s - V_l - ...
mama b's user avatar
  • 83
1 vote
1 answer
175 views

How to use the equivalent circuit of an induction motor?

I have met a data sheet for a three phase induction motor intended for the traction applications. The data sheet contains below given table I have chosen the column operating point - continuous point ...
Steve's user avatar
  • 1,113
1 vote
1 answer
240 views

Explanation of 4-wire Delta Transformer Phasor Diagram

I have been studying some of the Tx configurations for metering. I've been looking at a booklet called the Power Measurements Handbook, which is sort of an informal resource in the metering world. I ...
compto2017's user avatar
0 votes
1 answer
60 views

How can I find the I1 phase angle provided?

A 240/110V transformer has a no-load primary current of 0.2A. When a purely resistive load is connected to the secondary, the primary current is 1.5A. Ignoring all losses and leakage effects, find the ...
B Hart's user avatar
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2 votes
1 answer
125 views

Find the voltage and the current in the circuit

Find \$v_2(t)\$ and \$i_5(t)\$ Data: \$i_4(t)= 3\cos(2t+150^\circ)\$ Solution: \$v_2(t)= 68.807\cos(2t+7^\circ)~\mathrm{mV}\$ \$i_5(t)= 2.481\cos(2t-177^\circ)~\mathrm{A}\$ What I need is the ...
Anthonengine's user avatar
0 votes
0 answers
39 views

Does a phasor of composite sinusoid give information?

I have a circuit with multiple supplies and each power supply has a different frequency. Would adding the rectangular form of the output give useful information about the composite sinusoid waveform? ...
Arcadius's user avatar
1 vote
1 answer
73 views

Please explain solution (TEM waves in spherical coordinates)

I have a question and a solution, I don’t know how the solution came up with the variables and values highlighted in blue in the solution part. Question: Solution:
zappi's user avatar
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0 votes
1 answer
260 views

Why do I get the wrong phase shift?

I am trying to compare theory vs simulation values and it seems to be that there are differences. I am using Multisim to simulate a RLC circuit, the LC are in parallel and in series to the resistor. ...
Arcadius's user avatar
2 votes
2 answers
121 views

Phasor of transfer function

Say I have the following transfer function: $$\mathcal{H}(s) = \frac{Bs^2}{a^2 + \frac{a}{Q}s +s^2}$$ I want to prove it is a Low-Pass filter. In order to do it I'd like to change it to phasor form so ...
ludicrous's user avatar
  • 1,163
0 votes
0 answers
131 views

Phasor format vs time domain format question

I have a quick question regarding phasor format vs time domain format. Whenever we write in the phasor format, the magnitude that we use must be the RMS value for voltage/current, correct? Then we ...
RItaPoon's user avatar
1 vote
1 answer
155 views

Why is the instantaneous magnitude of current and voltage in a phasor diagram given by the vertical components of the phasor vectors?

In general, if a phasor is rotating, the instantaneous voltage is given by \$i_m\sin(\omega t)\$ where \$i_m\$ is the amplitude of the current. Similarly, voltage is given by \$v_m\sin(\omega t)\$ ...
math and physics forever's user avatar
2 votes
1 answer
355 views

Phasor calculation doubles frequency?

When working with phasors we have $$\bar{Z} = A\cos(\omega t + \phi) = Re(Ae^{j(\omega t + \phi)}) = Re(Ae^{j\phi}e^{j\omega t})$$ where $$\bar{P}_1 = Ae^{j\phi}$$ is the phasor. But when we multiply ...
ludicrous's user avatar
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13 votes
5 answers
2k views

What is the imaginary part of a phasor expressing?

Lets say we have a sinusoidal signal in the form \$V = A e^{j\omega t}\$ We can also write this as \$V = A(\cos(\omega t) + i\sin(\omega t))\$ If we plot this signal, we see the real part of above ...
BenK's user avatar
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0 answers
408 views

Current source in parallel with a short circuit

If a Dependent current source is placed in parallel with a short circuit, to solve our calculations would we assume that no current will flow through the dependent source and hence we remove it. For ...
Sherry's user avatar
  • 1
2 votes
1 answer
231 views

Why is one current reading ~20% higher than the other two in a balanced high-leg delta load?

We are using eGuage watthourmeters to monitor the outdoor unit on five VRF systems powered by two different 3P4W 120/208V high-leg delta panels. The neutral is not connected to the outdoor units. We ...
LShaver's user avatar
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1 vote
1 answer
204 views

How can I solve the following phasor analysis question?

How can I solve part B? Obviously, since the two sources have different frequencies I started off by killing the voltage source (short-circuit) and then tried to apply KCL. My goal was to find the ...
Ahsan Yousaf's user avatar
0 votes
1 answer
273 views

Series RLC circuit - Phase difference between voltages across inductor and resistor is not exactly 180, why?

In phasor analysis we put inductor voltage along positive \$j\$ axis and capacitor voltage along negative \$j\$. So these two voltages are exactly \$180\$ degrees apart. But in simulation below, the ...
across's user avatar
  • 1,150
4 votes
0 answers
254 views

How does a driving voltage affect an LC circuit?

I need help understanding how the drive voltage \$V_d\$ and the coupling capacitor \$C_d\$ in the circuit above affect the total energy of the LC circuit. The author arrives at the following equation ...
bubakazouba's user avatar
0 votes
2 answers
617 views

CT showing different reading at phase and neutral

simulate this circuit – Schematic created using CircuitLab I have attached a simplified version of my test circuit. When the current transformer is connected to the neutral side like in the ...
Sadat Rafi's user avatar
  • 2,519
0 votes
2 answers
962 views

Why use vector sum for calculating neutral current?

In a three phase system, we use a vector sum to calculate resulting neutral current. I don't understand why we use vector sum. The resulting neutral current is actually the sum of instantaneous values ...
user299763's user avatar
0 votes
0 answers
275 views

Combined Space and Time Phasor Diagram of a Synchronous machine

Consider a synchronous generator with its electrical and mechanical angles between them In the left diagram δ is in mechanical domain but delta is also the electrical angle between Ef and Er in the ...
Nigel Goveas's user avatar
0 votes
1 answer
194 views

Phasor angle calculation

In this example, for Vo it first says it is lagging by -134.8 degrees, however when then calculating actual Iin, the angle for Vo becomes -138.4. I'm wondering if -134.8 is a typo, and if it isn't; ...
Anna Smith's user avatar
0 votes
1 answer
102 views

Does Clarke transformation convert scalar quantity to vector quantity?

Current is a scalar quantity, is it converted to vector quantity using Clarke's transformation? If it is correct, I would like to know how transformation converts from scalar to vector? Thanks and ...
Ethan's user avatar
  • 43
0 votes
2 answers
800 views

Phasorial notation

In the phasorial notation (of a voltage or current, for example), should i use the peak value of a sinusoidal wave or its effective value (rms)? I ask this, because i get confused after reading some ...
Murilo's user avatar
  • 115
1 vote
2 answers
205 views

KVL in the frequency domain - Why is the sum of phasors 0 and not just the real part of the sum?

In many proofs of Kirchhoff's voltage law for the frequency domain, the time-domain KVL is originally used and then the time-dependent part (\$e^{jwt}\$) is removed, leaving only the real part of the ...
Gary Allen's user avatar
0 votes
2 answers
470 views

About simulating an ac circuit in Pspice

Firstly, It's not homework. I already know the answer. But I couldn't see sinusoidal waves to calculate phase of voltage(V0) across the capacitor. Response of capacitor is look like damping. However, ...
bahadir3301's user avatar
1 vote
1 answer
561 views

Phase angle of sine wave (confusion)

Usually, phasors are represented by Acos(ωt + φ) where φ is the phase angle. Using this convention, we need to convert sin(ωt) into cos(ωt - 90) to get its phase angle like this thumbnail on a YouTube ...
Elrond's user avatar
  • 33
1 vote
1 answer
526 views

Differential Equations vs Phasor vs Laplace

I've just read a book on basic circuit theory and I'd like to understand the pros and cons of each analysis method. Time Domain Usually ends up in differential equations for reactive circuits. Gives ...
jaurunjljgrtutkwcy's user avatar
1 vote
1 answer
479 views

Band stop filter RLC circuit frequency response

Assume we have an $ RLC $ circuit as described in the picture This should be a Band-stop filter. But somethings bother me in my calculations. This is my calculations for the frequency response: Using ...
FreeZe's user avatar
  • 173
1 vote
1 answer
1k views

Explaination on phasor diagram for RL circuit?

This is the phasor diagram which I had drawn from the value of phase difference(deg) from MULTISIM. I'm a bit confuse here... shouldn't by theory, when inductance is increase, thus the degree for Vl ...
Nazfull's user avatar
  • 21
0 votes
1 answer
1k views

Why voltage in capacitor lags behind the source voltage in RC circuit?

Voltage across the capacitor lags behind the current through capacitor as we know. But why the voltage across the capacitor lags behind the source voltage in this circuit ? Similarly it is found that ...
Alex's user avatar
  • 1,498
3 votes
1 answer
7k views

Converting from time domain to phasor domain?

If I have a voltage source of a circuit \$V_s(t) = 8\cos(24\pi*10^9t-60^{\circ})\$ (V) and I want to convert it to the phasor domain would it be this? \$8e^{-j60^{\circ}}\$?
Geno C's user avatar
  • 341
0 votes
3 answers
380 views

IQ modulation and phasors: which first?

Do we use IQ modulation because quadrature signals are a good physical implementation of phasors - or is it the other way around? To elaborate a little:I'm having a hard time getting a clear ...
John B's user avatar
  • 223
0 votes
2 answers
329 views

Why is the phase angle in the summation of the phasors the negative arctan?

I was reading a textbook and came across the following $$ \\I_1 = Ae^{j0} = A \\I_2 = Be^{-j\frac{\pi}{2}} \\\bf{I} = I_1 + I_2 \\If\ A=10\ and\ B=20 \\|I| = \sqrt{A^2 + B^2} \\\angle I = -tan^{-1}(B/...
Shankar Ramharack's user avatar
1 vote
1 answer
90 views

Can AC harmonic quantities be expressed as a sum of phasors of different frequencies without confusion?

https://www.electronics-tutorials.ws/accircuits/harmonics.html The problem with AC harmonics is that each term has a different frequency, being a integer factor of the first frequency. I was wondering ...
AndroidV11's user avatar
1 vote
1 answer
122 views

What am I doing wrong in finding the phase angle of power?

Consider a voltage supply \$V\angle \phi_1\$ and a circut with impedance \$Z \angle \phi_2\$. Now the Apparent power(\$S\$) is given by: $$\bar S =\frac{(\bar V)^2} {\bar Z}$$ Thus phase angle of \$S\$...
Ronald Becker's user avatar
0 votes
0 answers
128 views

is it possible for the phase difference between voltage and current to exceed pi/2 in a RL circuit?

I did an experiment where I made a RL circuit. My IV was resistance and DV was phase difference between voltage and current. To find the phase difference, I took the difference (Δt) between time when ...
butterchickencurry's user avatar
0 votes
1 answer
149 views

Phase-shift a Broadband Time-Domain Function

Suppose we have an operator \$A_\phi\$ which phase-shifts a sinusoid by \$\phi\$: $$A_\phi[\cos(\omega t)] = \cos(\omega t + \phi)$$ In phasor domain, \$A_\phi = e^{+j\phi}\$ is a complex constant. I ...
Argon's user avatar
  • 101
1 vote
3 answers
964 views

Why can't circuit breakers close across a large phase angle difference?

In power systems I understand that breakers have mechanisms preventing their closing if they detect the phase angle (and voltage) across them to be too large. This is usually called a 'sync check'. ...
ZekeC's user avatar
  • 486
2 votes
1 answer
275 views

RMS values and Phasors

I need to solve these two exercises but I really have no idea where to start. How should I proceed to solve this kind of problems? I tried to find something on my teacher's files but haven't ...
user avatar
1 vote
1 answer
264 views

How do I transform this sinusoid in phasor?

If it is a signal like this i(t)=5*sin(100t-pi/3)A, I know how to transform. But how do I do this e(t)=2-√(2)*sin(10t+pi/4) ? I meant I don't know what to do with "2-" Thanks for the help!
Christofor15's user avatar
3 votes
3 answers
2k views

How to calculate rotor flux of the three phase squirrel cage induction motor?

I have a three phase squirrel cage induction motor with given parameters (stator winding connected in delta) nominal power: \$P_n = 22.4\,\mathrm{kW}\$ nominal stator voltage: \$V_{sn} = 230\,\mathrm{...
Steve's user avatar
  • 1,113
0 votes
1 answer
131 views

RC circuit - phase current

I have a simple RC circuit as below : I'm trying to visualize current curve and voltage curve (Vout and I(R1)) vs Vin using LtSpice and I obtain the result below: It's OK that the Vout is leading ...
geek225's user avatar
  • 197
0 votes
4 answers
169 views

can I also use phasors/concept of impedances for non sinusodial signals?

I know that phasors are great to solve circuits driven by sinusodial input signals but I was wondering if I can incorporate phasor concepts(like impedance) to circuits driven by input signals not ...
EEguy's user avatar
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