phasor and phasor relationships of circuit elements

[PG1995]

Hi

Please first have a look on the link titled Q1; it will tell you how to use other two links. Please help me with the queries. Thanks a lot.

Q1: https://img46.imageshack.us/img46/5341/phasorstrip.jpg
Q2 and Q3: https://img38.imageshack.us/img38/9113/phasor2222.jpg
Ref #1: https://img535.imageshack.us/img535/5140/imgxp.jpg

Regards
PG

 

[MrAl]

Hi,

You can use degrees in phasors as long as you remember to use the little degree sign. Thus:
e^(j pi/4) = e^(j 45 º)
(hope that renders right in your browser, but if not the 45 has a little degree sign after it).

The imaginary operator i represents a rotation of 90 degrees, and for 1/i we multiply top and bottom by i so we get i/-1 which equals -i, and yes that is -90 degrees.
Since you are asking this question it might be a good time for you to look into the two argument inverse tangent function which is sometimes shown as:
atan2(y,x)
Note that the inverse tangent is often shown as:
atan(x)
and note there is only one argument there, the x.
But with atan2(y,x) there are two arguments, y and x. That means it takes two arguments to calculate the inverse tangent. This is necessary because the single argument atan(x) function can not discern between different quadrants, but because atan2() has two arguments it can, and so provides the correct phase angle while atan() always has to be adjusted manually. If you dont understand now is a really good time to look into it. It isnt hard i assure you, and will answer many of your future questions about phase angle in circuits and all.
For your question about 'i' for example, we would look at the complex plane and see that i is along the 'y' axis, so that is the first argument in atan2(y,x). So we would have
phase=atan2(i,x) with i the complex operator. Now since the real part of i is zero, we would want to do this:
phase=atan(i,0)
and the result here is phase=90 degrees.
Similarly, using -i in place of i we would get phase=-90 degrees.