25,330

[kopcicle]

What is the resonant frequency of a series RLC circuit if R = 22 ohms, L is 50 microhenrys and C is 40 picofarads? Let's see....

There is a very useful formula for resonance: Capacitance in pF times inductance in uH equals 25,330 divided by frequency in MHz squared.

LC = 25,330/F^2

Or, rearranged:

F^2 = 25,330/LC

50 x 40 is 2000.

25,ooo divided by 2 is 12,500
330 divided by 2 is 165
So 25,330 divided by 2 is 12,665

12,665 divided by 1000 is 12.665

Square root of 9 is 3. Square root of 4 is 16. So the resonant frequency is somewhere between 3 and 4 MHz.

was just futzing around with a tank circuit and...

 

[Beetle]

This is how I learned it. The resistance doesn't matter; resonance is determined by the value of inductive reactance coupled with an equal (but with the opposite sign) value of capacitive reactance.

 

[Shadetree Mechanic]

You guys are making my brain hurt. Way too early and I have only had one cup of coffee......

 

[Captain Kilowatt]

This is how I learned it. The resistance doesn't matter; resonance is determined by the value of inductive reactance coupled with an equal (but with the opposite sign) value of capacitive reactance.

That's the way I learned it as well. You are correct in that resistance will not change the resonant frequency however it can limit the peak resonant frequency.

 

[Handy Andy]

What is the resonant frequency of a series RLC circuit if R = 22 ohms, L is 50 microhenrys and C is 40 picofarads? Let's see....

There is a very useful formula for resonance: Capacitance in pF times inductance in uH equals 25,330 divided by frequency in MHz squared.

LC = 25,330/F^2

Or, rearranged:

F^2 = 25,330/LC

50 x 40 is 2000.

25,ooo divided by 2 is 12,500
330 divided by 2 is 165
So 25,330 divided by 2 is 12,665

12,665 divided by 1000 is 12.665

You were doing fine until I got to here...

Square root of 9 is 3. Square root of 4 is 16. So the resonant frequency is somewhere between 3 and 4 MHz.

was just futzing around with a tank circuit and...

Welcome to Core learning - it's not how you got to the answer, just that you did...

BTW = SQRT(16) = 4

Because 4^2 = 16...

SQRT(4) = 2
Because 2^2 = 4

Did you mean 2 to 3 MHz or thereabouts...?