# How to compute the quality factor in parallel RLC circuit

#### antiantianti

Joined Aug 4, 2016
45
Hi
I have a hard time solving this problem in AC circuit
the question is to compute the quality factor of the whole circuit when given the values of L ; Q1 , Q2 , C, and R.
I even have the answer but I dont understand it
Thank you

#### Motanache

Joined Mar 2, 2015
521
Start by calculating the quality factor of a parallel RLC circuit is a lot of documentation on the Internet.

If L has Q1 it means that L has internal resistance.

Try to understand the quality factor = it's more important than the grade or solving the homework

#### Picbuster

Joined Dec 2, 2013
1,026
As you understand that quality is a term to identify how good something is.
Also applicable to oscillating processes.
Now it's up to you to combine this information with your parallel oscillating circuit.
Your question is: which component(s) is /are effecting the quality?

Picbuster

#### JoeJester

Joined Apr 26, 2005
4,390

#### Motanache

Joined Mar 2, 2015
521
There are quite a many formulas and seemingly complicated,
My advice is to learn some simple ones to withdrawn the rest.

E.g. RLC parallel
Equivalent parallel resistance is calculated as follows:
1/R=1/R1+1/R2+...............................

Its equivalent in AC is impedance:

It's the same. But keep in mind that the impedance is a complex number.

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#### JoeJester

Joined Apr 26, 2005
4,390
Is the thread starter going to show the question with the values they are given?

#### Motanache

Joined Mar 2, 2015
521
R, XL and XC are known.
Why is the impedance a complex number? The imaginary part are reactive effects.

For example on a capacitor I can measure the voltage on it. That's the real part Re(Z)
But that capacitor stored energy. This is the imaginary part Im(Z).

https://en.wikipedia.org/wiki/Q_factor
"In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is,[1] and characterizes a resonator's bandwidth relative to its centre frequency.[2] Higher Q indicates a lower rate of energy loss relative to the stored energy of the resonator; the oscillations die out more slowly. A pendulum suspended from a high-quality bearing, oscillating in air, has a high Q, while a pendulum immersed in oil has a low one."

Q=energy stored/ energy dissipated per cycle
Where does energy is dissipate? Only the resistor can heat up.
As I said before:
If the coil has a given quality factor of its own, it means it has its own electrical resistance, which will be considered in series with it.
The capacitor also has ESR.

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#### JoeJester

Joined Apr 26, 2005
4,390
R, XL and XC are known.
Where has the thread starter published the knowns? Where has the thread starter published their work? The thread started said they "have" the answer, does that mean it was given to them or the answer he calculated agreed with a published answer?

If they need a math refresher, they can get one at http://www.tech-service.net/Math/mathematics.html by downloading the book associated with question.

#### Motanache

Joined Mar 2, 2015
521
Question for the initiator of the discussion: if you design an radio and the RLC circuit gives the reception frequency, we want the quality factor of this circuit to be as big or as small as possible?

OR:

I know the rule is not to give answers.
But I advise him if he wants to study electronics: the capacitor, coil and resistance will meet them very often.

Electronics is beautiful. But some articles seem difficult because even the author who wrote them did not really understand what he wrote,

.

#### JoeJester

Joined Apr 26, 2005
4,390
Hi
I have a hard time solving this problem in AC circuit
the question is to compute the quality factor of the whole circuit when given the values of L ; Q1 , Q2 , C, and R.
I even have the answer but I dont understand it
Show the problem and show your work.

Read the two references from post number 4. Write down any and all questions, and post them.

#### JoeJester

Joined Apr 26, 2005
4,390
If the coil has a given quality factor of its own, it means it has its own electrical resistance, which will be considered in series with it.
The capacitor also has ESR.
Those would be stated as part of the problem. I'm waiting for the thread starter to post something.