Maths question.

[Dr Jekyll]

I have two equations. A = 2Pi * F * L, and B = 1/(2Pi * F * C).

What I’d like is one equation that given values of C and L, tells me what value of F makes A = B but i can't see how to create it.

These are both equations used in electronics, particularly radio. The first one tells you the ‘reactance’ (effectively the resistance) of an inductor at a given frequency. F being the frequency and L being the value of the inductor. The second gives the reactance of a capacitor at a given frequency, C being the value of the capacitor.

The idea is that if both components are in a circuit they will either block or pass a specific frequency depending on how they are wired up. That frequency being the one where reactance is the same for both components. That’s why I’d like one equation that I can plug L and C into and read the value of F where A = B, without worrying about what A and B are except for being the same.

(Taking a few liberties with terminology here to avoid getting bogged down with matters irrelevant to the algebra)

[Mr Pointy]

f=1/2π√(LC) maybe?

[Scarletpimpofnel]

Mr Pointy said:

f=1/2??(LC) maybe?

Yup that's what I got too. Band pass filter I guess.

[TonyRPH]

This looks wrong (I seem to get a different result on my calculator too so perhaps it's my lack of Excel skills or just total lack of maths skills - more likely!)....

Cell C2 : =(2*3.1415927*B2*(B3/1000))

Cell G2 : =1/(2*3.1415927*F2*(F3/1000))

Cell B5 : =1/(2*3.1415927)*SQRT(C2*G2)

Where did I go wrong?

[Scarletpimpofnel]

I think it's right what was given before. This from the web suggests the same -

[Dr Jekyll]

Thanks everyone.

[GTS_uk]

Made me smile seeing this.
I did a military electronics apprenticeship in the 90s and the lecturer drummed this into us “singing”

“1 over 2 Pi root LC - That is the resonant frequency”

IYKYK

😂

[EddieSteadyGo]

I've been experimenting with ChatGPT, just to see what it can do. I entered your post into chatgpt and it understood the context, provided background information on both equations and solved it too.

This is the final part of its reply. Quite good that it can interpret equations and rewrite them without being overly pedantic on the initial form of what it is provided.

[Scarletpimpofnel]

That's impressive AI. The thing I guess you'd have to use that AI many many times before you could trust what it was telling you was correct. Maybe it got that bit of maths correct but 100 other examples hopelessly wrong? I don't know as I have never used it!

[paulrockliffe]

Scarletpimpofnel said:

That's impressive AI. The thing I guess you'd have to use that AI many many times before you could trust what it was telling you was correct. Maybe it got that bit of maths correct but 100 other examples hopelessly wrong? I don't know as I have never used it!

Yes, but if you can check the answer, its a lot quicker than working it out yourself.

[EddieSteadyGo]

Scarletpimpofnel said:

That's impressive AI. The thing I guess you'd have to use that AI many many times before you could trust what it was telling you was correct. Maybe it got that bit of maths correct but 100 other examples hopelessly wrong? I don't know as I have never used it!

It wasn't a lucky guess.

For my company, when we employ potential candidates we ask them to take a numerical test. Questions are not hard maths, but require some basic numeracy.... example question would be something like, "two runners compete over an 8 mile course, 5 miles uphill and 3 miles down. ‘John’ ran 6 mph both up and down, ‘Sarah’ ran 3 mph uphill and 12mph downhill. Who came first?"

If I paste this exact question (with no editing or additional context) I get the following answer within 3 seconds....

[Simpo Two]

When calculators were invented, people stopped doing mental arithmetic.

When spellcheckers were invented, people stopped spelling.

When people are plugged into AI, will they stop thinking?