# Complex number/Argand diagram questions.

Hi all,

I'm doing an engineering course and have a question that's kinda stumped me.
I'm not going to post the actual question as i prefer to try and work it out myself....I've managed everything else so far,,,just this one is proving a bit of a noggin-scratcher....I just need a few questions answering/pointers in the right direction!

## Homework Statement

:[/B]

The question stated that the pd across a circuit is given by two complex numbers, one for Voltage, one for current.

## Homework Equations

:[/B]

a. 'sketch the appropriate phasors on an argand diagram'
b. Find the phase difference between the phasors for V and I
c. find the power from another given equation. (p=V x I x cosθ)

## The Attempt at a Solution

Questions as follows-

none of the circuit components/values are stated so I'm presuming the quoted complex numbers are the final resultants...if so then is it as simple as just plotting the phasor diagram and then converting to polar form to get the phase angles, from which they can be subtracted to get the V and I phase difference?

As both V and I have phase angles how are these plotted on the same argand diagram?? - I've read that one has to be the 'reference' phasor running along the x axis..if so and it's plotted on the 0 phase angle, do we take it's 'real' phase angle into account when plotting the other phasor?
For example - if V has 20° lead, and I has 10° lead, if we use I as ref do we plot V at 10° (20 - 10)?? (as I's lead would be from starting from 'under' the X axis at this point).
Or do we just leave a ref out as they both have phase angles and just take them both from the X-axis?
I've tried looking up argands for combined V and I plots but cant find anything decent.
How can we actually plot V and I together if , for example V is few hundred volts but I is in miliamps? Can they actually BE plotted together on the same diagram in a case like this?
Any links or examples would be gratefully appreciated.

Finally, is it as simple as taking the phase angle and 'plugging it in' with the relevant V and I?

I'm slightly worried as this is how I would have worked out the phase differences and power, but it seem a bit ...'too easy'.

Any help or pointers would be greatly appreciated.

Last edited:

berkeman
Mentor
Hi all,

I'm doing an engineering course and have a question that's kinda stumped me.
I'm not going to post the actual question as i prefer to try and work it out myself....I've managed everything else so far,,,just this one is proving a bit of a noggin-scratcher....I just need a few questions answering/pointers in the right direction!

## Homework Statement

:[/B]

The question stated that the pd across a circuit is given by two complex numbers, one for Voltage, one for current.

## Homework Equations

:[/B]

a. 'sketch the appropriate phasors on an argand diagram'
b. Find the phase difference between the phasors for V and I
c. find the power from another given equation. (p=V x I x cosθ)

## The Attempt at a Solution

Questions as follows-

none of the circuit components/values are stated so I'm presuming the quoted complex numbers are the final resultants...if so then is it as simple as just plotting the phasor diagram and then converting to polar form to get the phase angles, from which they can be subtracted to get the V and I phase difference?

As both V and I have phase angles how are these plotted on the same argand diagram?? - I've read that one has to be the 'reference' phasor running along the x axis..if so and it's plotted on the 0 phase angle, do we take it's 'real' phase angle into account when plotting the other phasor?
For example - if V has 20° lead, and I has 10° lead, if we use I as ref do we plot V at 10° (20 - 10)?? (as I's lead would be from starting from 'under' the X axis at this point).
Or do we just leave a ref out as they both have phase angles and just take them both from the X-axis?
I've tried looking up argands for combined V and I plots but cant find anything decent.
How can we actually plot V and I together if , for example V is few hundred volts but I is in miliamps? Can they actually BE plotted together on the same diagram in a case like this?
Any links or examples would be gratefully appreciated.

Finally, is it as simple as taking the phase angle and 'plugging it in' with the relevant V and I?

I'm slightly worried as this is how I would have worked out the phase differences and power, but it seem a bit ...'too easy'.

Any help or pointers would be greatly appreciated.

If you also had the source voltage, you could plot that on the x-axis as a reference, but it sounds like you have been given the final voltage and current phasors, so just plot them both on the same polar complex plot. Don't worry about the scales being different -- you could always show a dual scale for the x & y axes if you needed to.

And yes, it does sound like you are given enough information so that the solution of the problem is pretty simple, I believe. This link may be helpful (the phasor discussion is near the end):

http://www.electronics-tutorials.ws/accircuits/complex-numbers.html