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transgalactic · 18th July 2009, 04:58 AM

for this signal
$ I_s(t)=sin(t) $
i have this equation
$ I_L(1-CL+jCR+jcz)=I_s $
then the next line is
$ I_L(1-CL+jCR+jcz)=j $

why they substitute j=I_s

aljamri · 18th July 2009, 06:21 AM

put in your mind that j = 90 Deg

transgalactic · 18th July 2009, 06:53 AM

no $j=\sqrt{-1}$

its not 90 deg

transgalactic · 18th July 2009, 07:37 AM

Quote:

Originally Posted by transgalactic

for this signal
$ I_s(t)=sin(t) $
i have this equation
$ I_L(1-CL+jCR+jcz)=I_s $
then the next line is
$ I_L(1-CL+jCR+jcz)=j $

why they substitute j=I_s

$ sin(t)=cos(\frac{\pi}{2}-t)=cos(t-\frac{\pi}{2}) $
the formula of the signal is
$ Is=Acos(\omega t+\phi) $
then we transform it to the phasor representation formula
$ Is=Ae^{j\phi} $
so we get
$ Is=1e^{-j\frac{\pi}{2}} $
and when we look at this expression as oilers formula we get
the Is=-j

so why its written Is=j
?

MrAl · 18th July 2009, 08:37 AM

Hi,

Isnt that just j*w with w=1?
sin(t) is sin(w*t) or sin(1*t).

For ac analysis, s is made equal to j*w
and j*w is used to represent a sinusoidal source.

aljamri · 19th July 2009, 06:01 AM

Quote:

Originally Posted by transgalactic

no $j=\sqrt{-1}$

and it is 90 deg

for example:

2j = 2 at angle of 90 deg

transgalactic · 19th July 2009, 06:06 AM

by what formula?

aljamri · 19th July 2009, 10:28 AM

Quote:

Originally Posted by transgalactic

by what formula?

without formula it is well known in Electrical engineering that the difference between 2 which means ( 2 ± 0j ) and 2j which means ( 0 + 2j ), is that although they are representing the same magnitude, but the are 90 deg apart. If you added them together, they gives 2 + 2j in rectangular form , which equals to 2.83 with 45 deg or in polar form.

complex number is explained in:

Complex Number -- from Wolfram MathWorld

check Euler formula link, you may find the answer for your problem.

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18th July 2009, 04:58 AM	#1
transgalactic	phazor question for this signal $<br /> I_s(t)=sin(t)<br />$ i have this equation $<br /> I_L(1-CL+jCR+jcz)=I_s<br />$ then the next line is $<br /> I_L(1-CL+jCR+jcz)=j<br />$ why they substitute j=I_s

18th July 2009, 06:21 AM	#2
aljamri	put in your mind that j = 90 Deg __________________ Its what your friend in Your mind, what you in your friends mind

18th July 2009, 06:53 AM	#3
transgalactic	no $j=\sqrt{-1}$ its not 90 deg Last edited by transgalactic; 18th July 2009 at 06:54 AM.

18th July 2009, 08:37 AM	#5
MrAl	Hi, Isnt that just jw with w=1? sin(t) is sin(wt) or sin(1t). For ac analysis, s is made equal to jw and jw is used to represent a sinusoidal source. Last edited by MrAl; 18th July 2009 at 03:18 PM.*