# phazor question

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#### transgalactic

##### Banned
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

##### Member
put in your mind that j = 90 Deg

#### transgalactic

##### Banned
no $j=\sqrt{-1}$

its not 90 deg

Last edited:

#### transgalactic

##### Banned
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
?

Last edited:

#### MrAl

##### Well-Known Member
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.

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#### aljamri

##### Member
no $j=\sqrt{-1}$
and it is 90 deg

for example:

2j = 2 at angle of 90 deg

by what formula?

#### aljamri

##### Member
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