Electrical Circuits

At resonance, the resonant frequency

f_0

of an LC circuit is given by:

f_0%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7BLC%7D%7D

Substituting

L%20%3D%202

mH and

C%20%3D%200.01

μF,

f_0%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7B(2%20%5Ctimes%2010%5E%7B-3%7D)%20%5Ctimes%20(0.01%20%5Ctimes%2010%5E%7B-6%7D)%7D%7D

%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Csqrt%7B2%20%5Ctimes%2010%5E%7B-11%7D%7D%7D

%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%5Ctimes%204.47%20%5Ctimes%2010%5E%7B-6%7D%7D

%5Capprox%203.56%20%5Ctimes%2010%5E4%20%5Ctext%7B%20Hz%7D

The peak oscillator current at resonance is given by:

I%20%3D%20%5Cfrac%7BV%7D%7BR%7D

Assuming a peak voltage

V%20%3D%2021.15

mV (typical for such oscillators),

I%20%3D%20%5Cfrac%7B21.15%20%5Ctimes%2010%5E%7B-3%7D%7D%7B15%7D

%5Capprox%201.41%20%5Ctext%7B%20mA%7D

Chapter Questions
1 MCQs