- #1

- 54

- 0

Q=Lw(sub 0)/R. So far I know that Q=w(sub 0)/delta but my professor used this formula to continue the derivation delta w=R/L and I don't know where it comes from. Can anyone give me a hint?

- Thread starter gazepdapi1
- Start date

- #1

- 54

- 0

Q=Lw(sub 0)/R. So far I know that Q=w(sub 0)/delta but my professor used this formula to continue the derivation delta w=R/L and I don't know where it comes from. Can anyone give me a hint?

- #2

marcusl

Science Advisor

Gold Member

- 2,755

- 406

Quality factor is defined by

Q= 2*pi*(energy stored in resonator)/(energy lost per cycle).

The peak stored energy is [tex]LI^2 / 2.[/tex]

The power dissipated in the resistance is [tex]I^2R/2[/tex], in terms of the peak current.

The time in one cycle is 1/f or, in terms of angular frequency, [tex]2\pi/\omega.[/tex] Putting these into the definition of quality factor gives

[tex]Q=\frac{\omega L}{R}.[/tex]

EDIT: clean up equation rendering and add following:

Note that this is true for a series LCR circuit. For a parallel circuit Q is one over the expression on the right!

Q= 2*pi*(energy stored in resonator)/(energy lost per cycle).

The peak stored energy is [tex]LI^2 / 2.[/tex]

The power dissipated in the resistance is [tex]I^2R/2[/tex], in terms of the peak current.

The time in one cycle is 1/f or, in terms of angular frequency, [tex]2\pi/\omega.[/tex] Putting these into the definition of quality factor gives

[tex]Q=\frac{\omega L}{R}.[/tex]

EDIT: clean up equation rendering and add following:

Note that this is true for a series LCR circuit. For a parallel circuit Q is one over the expression on the right!

Last edited:

- #3

- 54

- 0

thanks a lot

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 3

- Views
- 1K

- Replies
- 1

- Views
- 29K

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 2

- Views
- 14K

- Last Post

- Replies
- 8

- Views
- 3K

- Replies
- 5

- Views
- 5K

- Last Post

- Replies
- 1

- Views
- 2K

- Last Post

- Replies
- 8

- Views
- 850