Question

The inductance in the drawing has a value of L = 9.4 mH. What is the resonant frequency f0 of this circuit?

Answer 1

Answer:

The resonant frequency of this circuit is 1190.91 Hz.

Explanation:

Given that,

Inductance, $L=9.4\ mH=9.4\times 10^{-3}\ H$

Resistance, R = 150 ohms

Capacitance, $C=1.9\ \mu F=1.9\times 10^{-6}\ C$

At resonance, the capacitive reactance is equal to the inductive reactance such that,

$X_C=X_L$    

$2\pi f_o L=\dfrac{1}{2\pi f_oC}$

f is the resonant frequency of this circuit  

$f_o=\dfrac{1}{2\pi \sqrt{LC}}$

$f_o=\dfrac{1}{2\pi \sqrt{9.4\times 10^{-3}\times 1.9\times 10^{-6}}}$

$f_o=1190.91\ Hz$

So, the resonant frequency of this circuit is 1190.91 Hz. Hence, this is the required solution.