Question

. Find whether the discharge of capacitor through the following inductive circuit is oscillatory. C = 0.1µF,
L = 10mh, R 200 Ω. If Oscillatory, find the frequency of oscillation and resonant frequency

Answer 1

As per the given question,

$c=0.1\mu F$

$L=10mh =10\times 10^{-3}h$

$R=200\Omega$

$Z=\sqrt{R^2+{X_L-X_c}}$

Resonating frequency,

$\omega=\frac{1}{\sqrt{LC}}$

Now, substituting the values,

$\omega=\frac{1}{\sqrt{0.1\times 10^{-6}\times 10\times 10^{-3}}}$

$\Rightarrow \omega =\frac{1}{\sqrt{10\times10^{-10}}}$

$\Rightarrow \omega=\frac{10^5}{\sqrt{10}}$

$\Rightarrow 2\pi f =\frac{10^5}{\sqrt{10}}$

$\Rightarrow f=\frac{10^5}{2\pi \sqrt{10}}sec^{-1}$

$\Rightarrow f=\frac{10^5}{19.87}sec^{-1}$

$\Rightarrow f=5\times 10^3 sec^{-1}$