Resonate frequencies?

Question

OK. I'm given "What is the resonant frequency of a series RLC circuit if R is 56 ohms, L is 40 microhenrys and C is 200 picofarads?"

I'm supposed to get 1.78 MHz.

If I plug into 1/2*Pi*sqrt L*C, I get 0.5*3.14*sqrt(40*200) or sqrt 8000 or 89.44. So; 0.5*Pi = 1.57, * 89.44= 140.42. If I convert microhenerys and picofarads to henerys and farads values (.00004 and .0000000002) I get 151.3 I've been trying to learn this with what I could find online and don't have a text book for this specifically. Could anyone offer a suggestion?

Answer 1

f = 1/(2π√(LC))

f = 1/(2π√(40µ*200p))

f = 1/(2π√(80e-16))

f = 1/(2π(8.92e-8))

f = 1/56.2e-8

f = 0.0178e8 = 1.78e6 = 1.78MHz

Your mistakes appear to be in the formula you used.

f = 1/(2π√(LC)) is correct,

but you seem to have read it as (1/2)*(2π√(LC))

.