SOLUTION: been trying to figure this out for 2 days now. 26. When an r-f tank is operating within 10 per cent of its resonance frequency, the impedance of the tank can be foun

Algebra ->  Expressions -> SOLUTION: been trying to figure this out for 2 days now. 26. When an r-f tank is operating within 10 per cent of its resonance frequency, the impedance of the tank can be foun      Log On


   

Question 821461: been trying to figure this out for 2 days now.
26. When an r-f tank is operating within 10 per cent of its resonance frequency, the impedance of the tank can be found by the formula
"Z= Zr divided by the square root of 1+4Q^2(F-Fr/Fr)^2 "
where z,. is the impedance of the tank at resonance, F is the operating frequency, and FR is the resonant frequency. What is the impedance
of the tank if its impedance at the resonant frequency, 150MHz, is
60,000ohm and the Q of the tank is 125? The tank is operating at
142.5 MHz. F and FR are in hertz and Zr is in ohms.
... for some reason my formula won't copy. so i put it in " "
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I suspect the formula you meant is
Z=Z%5Br%5D%2Fsqrt%281%2B4Q%5E2%28%28F-F%5Br%5D%29%2FF%5Br%5D%29%5E2%29
With Q=125 , Z%5Br%5D=60000ohm , F%5Br%5D=150MHz , and F=142.5MHz ,
Z=60000ohm%2Fsqrt%281%2B4%2A125%28%28142.5-150%29%2F150%29%5E2%29
so Z=6000ohm%2Fsqrt%281%2B500%287.5%2F150%29%5E2%29
Z=60000ohm%2Fsqrt%281%2B500%2A0.5%5E2%29
Z=60000ohm%2Fsqrt%281%2B500%2A0.0025%29
Z=6000ohm%2Fsqrt%281%2B1.25%29
Z=60000ohm%2Fsqrt%282.25%29
Z=60000ohm%2F1.5
Z=40000ohm

NOTE:
%28F-F%5Br%5D%29%2FF%5Br%5D=%28F-F%5Br%5D%29%22%2F%22F%5Br%5D
When you can write is as %28F-F%5Br%5D%29%2FF%5Br%5D , those brackets are included in the horizontal line.
Typing the formula in one line without without those brackets gives it a different meaning:
F-F%5Br%5D%22%2F%22F%5Br%5D=F-F%5Br%5D%29%2FF%5Br%5D
and that is a big problem when entering calculations into a computer or calculator.