Mesh Analysis: Solving for I1 with Loop Equations

[shaltera]

i₂=(-100i1-j10)/25=-10(10i1-j)/25=-2(10i1-j)/5

i₂=-2(10(0.093<-98.86)-j)/5

Honestly I don't know how to continue

 

[gneill]

i₂=(-100i₁-j10)/25=-10(10i₁-j)/25=-2(10i₁-j10)/5

Okay, but simpler:

$i_2 = -4 i_1 - j\frac{10}{25}$

EDIT: and use the rectangular version of i₁ to plug in.

 

[shaltera]

i2=-4(0.093<-98.86)-j10/25=-4(-0.0143+j0.091)-j0.4=0.052-j0.364-j0.4=0.052-j0.764

 

[gneill]

Equation above have two unknown,if I replace i1 with 0.093<-98.86 look mess

Only i₂ is unknown. Convert i₁ to rectangular form before plugging it in.

Note that you should make a habit of keeping more digits in intermediate values! Otherwise repeated conversions and calculations will cause rounding and truncation errors to creep into your results (especially for angular values). Always keep extra guard digits!

 

[shaltera]

0.052-j0.764=sqr(0.052²+(-0.764)²tan ^-1(-(0.764/0.052)=0.765<-86.106

 

[gneill]

0.052-j0.764

What is that? If it's i₂ it doesn't look right. Show your steps.

 

[shaltera]

i1=0.093<-98.86

I converted polar form to complex numbers for i1
-0.0143+j0.091 then I entered in

i2=--4i1-j10/25
i2=-4(-0.0143+j0.091)-j0.4=0.052-j0.364-j0.4=0.052-j0.764
i2=0.052-j0.764=sqr(0.052²+(-0.764)²)tan ^-1(-(0.764/0.052)=0.765<-86.106

 

[gneill]

i1=0.093<-98.86

I converted polar form to complex numbers for i1
-0.0143+j0.091 then I entered in

Should be: -0.0143 - j0.0911
Check your conversion. You should note that an angle of -98.86° places it in the third quadrant, so both terms must be negative.

i2=--4i1-j10/25
i2=-4(-0.0143+j0.091)-j0.4=0.052-j0.364-j0.4=0.052-j0.764
i2=0.052-j0.764=sqr(0.052²+(-0.764)²)tan ^-1(-(0.764/0.052)=0.765<-86.106

 

[shaltera]

I calculated with Matlab

for I1=-0.0143-0.0911i=0.0922<-98.9040
for I2= 0.0571-0.0356i=0.0673<-31.9553

I don't get it why we have to calculate by hand?

 

[shaltera]

Can I use Matlab for my assessment?

a=[47+100j 100j;100j 25j]
b=[12;10]
i=a\b

then magn=abs(i)
and then the angle
angle(i)*180/pi

Why do we have to calculate by hand?I'm not living in 20 century

 

[gneill]

I calculated with Matlab

for I1=-0.0143-0.0911i=0.0922<-98.9040
for I2= 0.0571-0.0356i=0.0673<-31.9553

I don't get it why we have to calculate by hand?

Yes, those values look good. As to why you have to calculate by hand, I can only presume that there are "pedagogical reasons"; You'll have to ask your instructor.

 

[The Electrician]

Can I use Matlab for my assessment?

a=[47+100j 100j;100j 25j]
b=[12;10]
i=a\b

then magn=abs(i)
and then the angle
angle(i)*180/pi

Why do we have to calculate by hand?I'm not living in 20 century

Who says you have to calculate by hand? Your instructor? Many instructors will require you to calculate by hand for a while so that you learn how complex arithmetic works. But, after a while, you should be able to use modern software or calculators.

 

[shaltera]

Apart of Matlab, I do not have a calculator with atan2 function.I was looking for a formula to convert polar to rectangular form but all examples are with positive values

 

[gneill]

Many calculators have built-in polar to rectangular (and back) functions. They will accomplish the same thing.