I have a doubt in question GOHAN from competition Quick Code

doubt
gohan

#1

We had to find V(in)/V(out):

V(in)=Impedance*Current

The circuit given is RLC circuit with varying frequency of VOLTAGE(V(in)).

The correct solutions of the question considered

Impedance= Resistance +R(l)+R©

Now that’s the thing I don’t understand

Isn’t Impedance = sqrt(r*r+(R(l)-R©)^2)

Giving V(in)/V(out)=sqrt(r*r+(R(l)-R©)^2)/R©

now this equation will have it’s minima at s=1/sqrt(R(l)*R©)

Resulting in itf= r/R©=r*sqrt(c/l)

I don’t understand where I am going wrong.


#2

your approach is wrong

try using KVL(Kirchoff’s voltage law)

vin=i*(R+sL+1/(sC))

vout=i*(1/(s*C))

vin/vout=LCss+RC*s+1

which is a quadratic in s

if a = LC and b=RC and c=1
unique value is at s= -b/(2*a) [Knowledge of quadratic equations]

so s=-R/(2*L)

value of vin/vout at s=-R/(2L) is
1-(R
RC/(4L))

This 1-(RRC/(4*L)) is the output


#3

@hrishabh15 Sorry, I can’t reply to the comment since I am going to attach a screenshot. However, this was the exact doubt I had when I saw the problem.

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I can’t understand, how such an ambiguous problem did appear in a rated contest.


#4

That’s an AC circuit. I don’t think you can add Inductive and Capacitive Reactance with Resistance.


#5

Yeah that’s the thing, How can they say “They can’t comment on AC or DC”.
They clearly mentioned some varying S, Definitely it has has to be omega.


#6

Yep, exactly… I thought I am losing my grey cells over time… XD


#7

XDXD… yeah I know, Poorly framed question.


#8

Anyway Is there a way to report it or something??


#9

I don’t know… I think you should first notify the @admin or the moderators before reporting straight away.


#10

You can actually. Here Voltage source is considered as RMS (it is generally the case unless specified an AC source). So you can treat inductors and capacitors as equivalent resistors and apply all DC properties here.


#11

Ok!! Considering Voltage is Dc source, then isn’t it a open circuit because of Capacitor.