How to figure resonant frequency/inductance

[daveleonard]

I need help with this practice exam question. Not just the answer but the formula or process it takes to get there. I need to know the math.
"A series circuit consists of an inductance of 500uH and a capacitance of 400pf. What is the resonant frequence?
And:

Three identical inductors valued at 90 MiliHenrys are connected in parallel. The total equivalent inductance is?
I know the answer is 30 MH but what is the math that gets that answer?



Thanks a lot.

 

[WA0CBW]

Resonant frequency is 1 over two pi times the square root of the Inductive reactance times the capacitive reactance.

Inductors in parallel are like resistors in parallel, add their reciprocals. A trick with equal value inductors (or resistors) is to divide their inductance (or resistance) by the number of them. Example is 4 resistors (or inductors) of 100 ohms each is 100 divided by 4 or 25 ohms.

If using a calculator enter the first value, press the reciprocals button (1/x), press the + button, enter the value, press the reciprocals button, (repeat this for as many values) then press the = button and then press the reciprocals button.

 

[daveleonard]

Math

Thanks for the info but would you mind laying out the math physically? Its been a long time since high school. 1/2 pi, what does that mean? I get the sq root, a number times itself resulting in 500 in this case.
I am poor at math but willing to learn. Thanks

 

[ramal121]

WA0CBW is correct but words are kinda confusing. Unfortunately ascii typing doesn't lend itself to expressing formulas.

This would be the steps on a calculator:
1) take capacitance and times it by inductance (keeping the exponents correct, milli, micro etc.)
2) press the square root button
3) take result and times it by Pi (3.141 a constant. Ratio of circumference to diameter of a circle).
4) then times that result by 2.
5) Now you need the reciprocal, just hit the 1/X button to reveal resonant frequency.

If you need the look of an actual formula I could scribble out a jpeg or something.

 

[WA0CBW]

Thanks ramal121. It is hard to say it in words and the formula doesn't look right when typed in. As you said it should have been the square root of the capacitance and inductance not capacitive reactance and inductave reactance. Thanks!

 

[majoco]

Resonant frequency is 1 over two pi times the square root of the Inductive reactance times the capacitive reactance.

Huh? How do you work out the reactance if you don't know the frequency?

It's the square root of the capacitance times the inductance. In base units too, so the 500uH is .0005H and the 400pF is 0.0000000004F

 

[daveleonard]

Thanks Ramal121 for the details. Unfortunately at test time I won't be allowed to have a calculator with me so I need to try to get my head around some sort of math formula or maybe I can get close enough to guess. I think if I just memorize the five steps you gave me I can get close. Thanks.

Regards, Dave

 

[ramal121]

daveleonard,

You should be able to have a calculator to do the math with. You just need to prove there is no hidden memory that would automatically do it for you. Good luck to you.

majoco,

OK OK, you caught a slip up. We all brain poof once in a while. Good catch though. I had to go into my cerebral back room to confirm the formula. To be honest, if I need a simple tuned circuit I grab a cap and a coil, twist it together and use whatever test equipment to see what I get. A little more of this, less of that and voila I'm done. None of this pencil, paper and slide rule stuff for me anymore.

 

[n5ims]

Unfortunately at test time I won't be allowed to have a calculator with me so I need to try to get my head around some sort of math formula or maybe I can get close enough to guess.

From the ARRL "What to bring to an exam session" page (http://www.arrl.org/what-to-bring-to-an-exam-session):

7. A calculator with the memory erased and formulas cleared is allowed. You may not bring any written notes or calculations into the exam session. Slide rules and logarithmic tables are acceptable, as long as they're free of notes and formulas. Cell phone must be silenced or turned off during the exam session and the phones' calculator function may not be used. In addition, iPhones, iPads, Androids, smartphones, Blackberry devices and all similar electronic devices with a calculator capability, may NOT be used.

A good formula reference for the Extra Class License is this .pdf from K6RIA (http://k6ria.net/PDF/Extra/Amateur_Extra_Exam_Math_Equations.pdf). It shows the questions, the formulas used and how to plug in the correct numbers to solve them. Although it uses an older question pool, the formulas are still the same as well as how they are used are still the same. Only the specifics are different (the 64 picofarad cap may now be a different number for example).

 

[WA0CBW]

Thanks to everyone for the corrections to my wording. I knew it was wrong as soon as I hit the send key. So as to not confuse anyone lets see if I can get it right this time. Resonant frequency equals one divided by two pi times the square root of Inductance times capacitance. When teaching this formula (and many others as well) I prefer to say the formula matching the key strokes as they are entered into the calculator like ramal121 did above in his 1,2,3 step description.
BB

 

[daveleonard]

Thanks to all, I will memorize the formula.