 How to derive the formula for question Dr Geros Lab(GOHAN) in Quick Code

I am a bit weak in physics so I can’t derive the exact formula for given circuit in [GOHAN] but by looking at others submissions I found out that it is 1-((R^2C)/(4L)) but don’t know how they derived it. Can anyone explain it?

R = R

Rc = 1/SxC

Rl = SxL

Vin = (R+Rl+Rc)xCurrent

Vout = Rc X Current

Therefore:

itf = Vin/Vout = (R+Rl+Rc)/Rc

on simplifying

itf = s^2(LxC) + s(RxC) + 1

there itf is a parabolic equation, and we know it to be unique at (property of parabola explained below)

d(itf)/d(s) = s(2xLxC) + RxC = 0

s = -R/(2xL)

putting s for itf value you can get the formula

Reason for d(itf)/d(s) = 0

our equation corresponds to general parabolic equation

y = ax^2 + b^x + c

d(y)/d(x) gives slope of the parabola

a unique point d(y)/d(x) = 0

or more simply it is a property that at

x = -b/2a will be the unique point (If you dont understand differentiaion, then just remember the fact)

If you need more details then please refer to parabola and its properties in a mathematics book. and you can upvote it if this helped you, I can really use some points right now(but earned).

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Use Ohm’s law .
step 1 : Vin = I(R+sL+1/(sC)
step 2 : Vout= I/(sC)

Vin/Vout = RSC + (S^2)LC+1
Hence , S^2LC - SRC+1-V =0 , where V is Vin/Vout.
We will get single value of S when determinant is 0.
i.e.
R^2C^2-4(1-V)LC=0.
solving this you will get
V=1-R^2C/(4L)

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Nice to see you on discuss @shinchan6599 And about physics… Me too xD…

Yeah seems simple enough… but needs a little physics though… Some simple physics. Be happy that this was the series case and that we were asked for the inverse transfer function. In this case we get a nice quadratic equation rather than a rational function with poles. If you’re too lazy to derive stuff you can also just look up the transfer function or similar, e.g. the https://en.wikipedia.org/wiki/RLC_circuit#Laplace_domain

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yeah thanks I used to derive stuff by my own at high school but Now I don’t have any connection with physics much so mind is a little bit rusted about physics…
I can again do physics for sure… just a little look over stuff…
But I get very less questions over physics… so…
though U have a got a point… I also agree it was simple physics…

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