Vectors and definitions headache

question

  • left to right angle, up and down magnitude

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  • left to right magnitude, up and down angle

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Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/vectors-and-ac-waveforms/

From experience with common graphs about this subject, the left to right line is usually always the direction/angle/etc. not the amount/magnitude/etc.
Am I reading correctly where it says "The length of the vector represents the magnitude (or amplitude) of the waveform.." in the link above

It's really throwing me off, it's suppose to be like this:


ignore everything except the left to right line, which is the ANGLE/DIRECTION of the sine wave not it's magnitude.
left to right should be angle and up and down should be magnitude.
 
Last edited:

WBahn

Joined Mar 31, 2012
29,930
What "left to right line" are you talking about?

The sinusoidal waveforms you show are the amplitude as a function of time or some other variable (which is expressed in degrees in this case).

The vector you are talking about, known as a phasor, is merely a means of representing the two characteristic parameters of a sinusoidal waveform, namely the amplitude and the phase (the shift relative to some reference) in a convenient way.
 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
What "left to right line" are you talking about?

The sinusoidal waveforms you show are the amplitude as a function of time or some other variable (which is expressed in degrees in this case).

The vector you are talking about, known as a phasor, is merely a means of representing the two characteristic parameters of a sinusoidal waveform, namely the amplitude and the phase (the shift relative to some reference) in a convenient way.
The dotted one.
 

MrChips

Joined Oct 2, 2009
30,618


The diagram on the left is a graphical representation of Voltage as a function of time, i.e. V(t). This is not a vector.
The diagram on the right, i.e. the horizontal line from left to right and ending in the arrow head is the graphical representation of a vector.
The length of the line represents the amplitude of the vector.
The inclination of the line (zero in this case) represents the phase angle. Hence this is a vector of V-volts and 0-phase.
 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140


The diagram on the left is a graphical representation of Voltage as a function of time, i.e. V(t). This is not a vector.
The diagram on the right, i.e. the horizontal line from left to right and ending in the arrow head is the graphical representation of a vector.
The length of the line represents the amplitude of the vector.
The inclination of the line (zero in this case) represents the phase angle. Hence this is a vector of V-volts and 0-phase.
right but shouldn't it be the other way around because of how we use the graph in my original comment. the way we use it there is left to right is angle and up and down is magnitude.

And then to have to switch it when we talk about vectors.
 

MrChips

Joined Oct 2, 2009
30,618
right but shouldn't it be the other way around because of how we use the graph in my original comment. the way we use it there is left to right is angle and up and down is magnitude.

And then to have to switch it when we talk about vectors.
No.
A vector is a straight line drawn with a certain length and at a certain angle.



 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
No.
A vector is a straight line drawn with a certain length and at a certain angle.



I guess my issue is I am trying to relate your figure to this one




is it correct to say that in this figure that @ 0 degrees I have 6 volts + @ 90 degrees I have 8 volts.
sorry if this is repetitive and base but I just need to hear someone say yes.
 

MrChips

Joined Oct 2, 2009
30,618
If the vectors represent voltages at different phase angles, then yes, that is correct.
The sum of the two voltages will be 10V @ 53.13 degrees.

Here is another example of how the diagram above can be applied:

A boat is heading north at 8 mph and the cross current is 6 mph west to east.
What is the true velocity of the boat?
Answer: 10 mph, N 37°E
 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
If the vectors represent voltages at different phase angles, then yes, that is correct.
The sum of the two voltages will be 10V @ 53.13 degrees.

Here is another example of how the diagram above can be applied:

A boat is heading north at 8 mph and the cross current is 6 mph west to east.
What is the true velocity of the boat?
Answer: 10 mph, N 37°E
Ok, I think I'm getting it.
 

WBahn

Joined Mar 31, 2012
29,930
As a function of time, a sinusoidal waveform has the form

\(
v(t) \; = \; A \cdot \sin \( \omega t \; + \; \phi \)
\)

Thus there are three parameters that we need to know in order to plot the voltage as a function of time. We need the amplitude, 'A', we need the frequency, 'ω', and we need the phase, 'φ'. For a variety of reasons, we usually specify the frequency and it is it is the same for all of the signals (we have ways of dealing with it when this is not the case). So for a given signal we only need to specify the amplitude and the phase.

We often need to add two sinusoidal signals together.

\(
v_3(t) \; = \; v_1(t) \; + \; v_2(t)
\)

where

\(
v_1(t) \; = \; A_1 \cdot \sin \( \omega t \; + \; \phi_1 \)
\;
v_2(t) \; = \; A_2 \cdot \sin \( \omega t \; + \; \phi_2 \)
\)

We know that the equation for v3 is

\(
v_3(t) \; = \; A_3 \cdot \sin \( \omega t \; + \; \phi_3 \)
\)

and we know that the frequency is the same as the common frequency of v1 and v2. We only need to figure out what A3 and φ3 are.

We could do this using trig identities, but what we find is that the math works out the same as if we represent our amplitude and phases as vectors, add the vectors together as vectors, and then extract the amplitude and phase information from the result.

The vector that we need for v1 has a length of A1 and it at an angle, relative to the positive horizontal axis, an angle of φ1 counterclockwise. The same for v2 in terms of A2 and φ2. After we add them together, head to tail, to get our vector for v3, the length of the resulting vector gives us A3 and the angle from the positive horizontal axis gives of φ3.
 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
If the vectors represent voltages at different phase angles, then yes, that is correct.
The sum of the two voltages will be 10V @ 53.13 degrees.

Here is another example of how the diagram above can be applied:

A boat is heading north at 8 mph and the cross current is 6 mph west to east.
What is the true velocity of the boat?
Answer: 10 mph, N 37°E
MrChips
would you be so willing to answer another question as an extension of this one.
Allaboutcircuuits.com does not include the formula for how to get cos and sin from an angle in polar form in order to convert it into a rectangular form shown here:
https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/polar-rectangular-notation/

or here:

https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/complex-number-arithmetic/

in order to add or subtract a vector at whatever uncommon angle.
Would you know what those formulas are e.g. how to add/subtract polar vectors, how to find angle cos and sin to convert from polar to rectangular.
 
Last edited:

WBahn

Joined Mar 31, 2012
29,930
There are lots of sites out there that will walk you through how to add vectors and convert back and forth between rectangular and polar coordinates.

Do a Google (or other search engine) search for something like: polar to rectangular vectors

Look through the results on the first page and you will probably find something that clicks with you.
 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
MrChips
would you be so willing to answer another question as an extension of this one.
Allaboutcircuuits.com does not include the formula for how to get cos and sin from an angle in polar form in order to convert it into a rectangular form shown here:
https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/polar-rectangular-notation/

or here:

https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/complex-number-arithmetic/

in order to add or subtract a vector at whatever uncommon angle.
Would you know what those formulas are e.g. how to add/subtract polar vectors, how to find angle cos and sin to convert from polar to rectangular.

Answer: https://www.allaboutcircuits.com/video-lectures/working-with-phase-angles/
 

Thread Starter

Mac Rodriguez

Joined Mar 24, 2016
140
https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/vectors-and-ac-waveforms/

From experience with common graphs about this subject, the left to right line is usually always the direction/angle/etc. not the amount/magnitude/etc.
Am I reading correctly where it says "The length of the vector represents the magnitude (or amplitude) of the waveform.." in the link above

It's really throwing me off, it's suppose to be like this:


ignore everything except the left to right line, which is the ANGLE/DIRECTION of the sine wave not it's magnitude.
left to right should be angle and up and down should be magnitude.
Answer:
The arrow symbol is NOT ONLY magnitude. Even though it doesn't look like it, it ALWAYS has an angle from 0-360. the length of the arrow symbol is your distance (magnitude/volts) and the degree or angle it MOVES FROM and then TO is your direction (phase angle), and there ALWAYS is a angle/degree, even a ZERO degree angle.

EX. if the arrow symbol starts at 0 and arrow symbol POINTY end finishes with 1 in. distance in between, then that VECTOR (arrow symbol) has a 0 DEGREE direction (PHASE ANGLE) and a DISTANCE/length (MAGNITUDE) of 1 in. (e.g. 100 Volts).
So you have a VECTOR (arrow symbol) at 0 degrees and a 100Volts.
 
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