Amplitude of Analog Filter Question

[nao113]

Homework Statement

Calculate V/E of the circuit below. I tried to calculate this one, is it correct? Thank you

Relevant Equations

Vc = 1/jwC

Question

Answer;

 

[Baluncore]

That does not look right to me.
You have a potential divider.
Reactance; Xv = XL + XC;
But what is the sign of XC ?
Impedance; Ztotal = R + jXv
The output V = E * jXv / Ztotal

 

[nao113]

That does not look right to me.
You have a potential divider.
Reactance; Xv = XL + XC;
But what is the sign of XC ?
Impedance; Ztotal = R + jXv
The output V = E * jXv / Ztotal

How about this one?

 

[Baluncore]

2nd guessing will not educate you, nor solve the problem.
At the frequency where L and C are resonant, there will be a deep notch with V = 0.
How can XL + XC = 0 ?

 

[nao113]

2nd guessing will not educate you, nor solve the problem.
At the frequency where L and C are resonant, there will be a deep notch with V = 0.
How can XL + XC = 0 ?

thank you for the feedback, what do you mean by 2nd guessing? for `How can XL + XC = 0 ?` what should I do for that question? Did I got it wrong for my calculation?

 

[Baluncore]

What is the reactance XL of an inductor?
What is the reactance XC of a capacitor?

 

[nao113]

What is the reactance XL of an inductor?
What is the reactance XC of a capacitor?

based on my class, here it is

 

[Baluncore]

Notice the sign of the reactance.
https://en.wikipedia.org/wiki/Electrical_reactance#Capacitive_reactance

 

[nao113]

Notice the sign of the reactance.
https://en.wikipedia.org/wiki/Electrical_reactance#Capacitive_reactance

I see, I ll change it

 

[nao113]

Notice the sign of the reactance.
https://en.wikipedia.org/wiki/Electrical_reactance#Capacitive_reactance

How about now? I use -1/wC for Xv, is it okay?

 

[Baluncore]

Both XL and XC are imaginary. R is real.
So XL + jXC does not equal Xv. Both XL and XC lie on the same axis.
Xv = ωL - 1/ωC
Then you fail to divide.

 

[nao113]

Then, I remove the imaginary, how about it?

 

[Baluncore]

You must move more methodically and accurately.
You removed the j, but immediately ignored the negative sign, then forgot to divide.

 

[nao113]

You must move more methodically and accurately.
You removed the j, but immediately ignored the negative sign, then forgot to divide.

how about this? I am sorry, I am new in this area so kinda confused

 

[Baluncore]

I wouldn't multiply XL by j, and then divide XC by j . That does not seem fair.
Z = R + j X;
If you work on the reactance, X only, you can ignore j for the moment.
You are having problems with fractions.
X = ωL - 1 / ωC = ( ωC·ωL - 1 ) / ωC .

 

[nao113]

I am so sorry, I didn't realize it
I revised again

 

[Baluncore]

Resistance, real, is plotted along the x-axis, reactance, imaginary, is on the y-axis. Impedance is a point on the map, represented by a complex number. Below the x-axis is negative, so it is a capacitive reactance, above the x-axis is inductive reactance. Resonance lies on the x-axis, where reactance is zero.

You must introduce j when you write a complex impedance, because it keeps the orthogonal real and imaginary axes apart. Z = R + jX is prevented from becoming Z = R + X by the presence of j.

So in your second line you must carefully identify the reactance components with j .

 

[nao113]

is it? do I need to change plus to minus after R in Z total? Then for |V/E|, did I put quadrat and roots correctly? should. I also put root on the top?

 

[Baluncore]

Now you are going to need to propagate that R + j ( ) along the second line;
That is needed to keep the impedance orthogonal.

 

[nao113]

Now you are going to need to propagate that R + j ( ) along the second line;
That is needed to keep the impedance orthogonal.i

how about this? is this what you mean as propagate?

 

[Baluncore]

I think you need to brush up on your complex arithmetic.
https://en.wikipedia.org/wiki/Complex_number

V = E * ( 0 + j Xv ) / ( R + j Xv )
So you need to divide an imaginary by a complex.

 

[nao113]

I think you need to brush up on your complex arithmetic.
https://en.wikipedia.org/wiki/Complex_number

V = E * ( 0 + j Xv ) / ( R + j Xv )
So you need to divide an imaginary by a complex.

Thank you very much, I see, I think my answer is still not correct. I ll try to learn your suggestion.