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mesh current method

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andymarra

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Hi there, first time post. I wasn't quite sure what category to put this under so apologies if its in the wrong section. Basically, part of my uni course is electronics and some of the mesh current method questions involve complex numbers, mainly the use of j and other things. I would get the answer as the solution gets it down to 4-j7 and then it says this equals 8.0623<-60.2551° .................................................. ...........< is supposed to be like/_ but couldnt find the proper symbol. I just cant understand the meaning of j and such things. How does it get from 4-j7 to this other answer?
Thanks, Andy
 
4-j7 is the complex number in rectangular format, and 8.0632^60.2551° is the complex number in polar format. Look at this for how to convert from one from to the other.

If you don't understand complex numbers then you need to learn about them. They are the basis for all AC circuit current and AC impedance calculations. Try Google.
 
Hello,


Yes i agree. I also could not find the little angle sign used to show angles.

A complex number is made up of at least two parts:
1. That which is called the 'Real' part, and
2. that which is called the "Imaginary" part.

The imaginary part is multiplied by the complex operator "j" (or in pure math they use "i") and then the two are shown as being added (or subtracted) and that makes up the complex number.

For example, if you have 4-j7 then that means that 4 is the 'real' part and -7 is the 'imaginary' part.

To get to the polar form, you calculate the 'Amplitude' and the 'Angle', then write them as
(Amplitude,Angle)
or replace the comma in the above with the little angle sign used to show angles.

To get the amplitude we use:
Ampl=sqrt(real^2+imag^2)

where 'real' is the real part and 'imag' is the imaginary part. Notice all we do there is square both parts and add them together, then take the square root.

To calculate the Angle, we use:
Angle=taninv(imag/real)

however to get the true phase angle you have to take the complex plane into consideration, or use the two argument form of the inverse tangent:
Angle=taninv(imag,real)

Lets do that example of 4-j7 which i will flip the -j7 to -7j to make the imaginary part clearer:
4-7j

Again the real part is 4 and the imag part is -7...

The amplitude is:
Ampl=sqrt(4^2+(-7)^2)=sqrt(65)=8.0622577 approximately.

The true phase angle is:
Angle=taninv(imag/real)=taninv(-7/4)= -60.255 degrees approximately, and noting that the point (4,-7) is in the fourth quadrant, no adjustment is needed as -60.255 is also in the fourth quadrant of the complex plane.


Thus we have the polar form:
(8.06,-60.255)

which is usually written with the little angle sign in place of the comma above, and always the amplitude is written before the angle.

Just one little caution is that you absolutely have to consider the complex plane when you calculate the true phase angle or else you have to use the two argument form of the inverse tangent function if it is available on your calculator or in your math program.

Just a quick little example of what could go wrong if we dont take this last precaution...

Say we have real part -4 and imag part -7, which is almost the same as before but now the real part is negative too.
Calculating the Angle:
Angle=taninv(-7/-4)=taninv(7/4)=taninv(1.75)=60.255 degrees
and now we note that 60.255 degrees is in the first quadrant but the point (-4,-7) is in the third quadrant, so this must be adjusted by:
TrueAngle=60.255-180= -119.7 degrees approximately.

This means the polar form of -4-7j is (8.06,-119.7)
(or again use the little angle sign in place of the comma).
 
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