Question

A condenser of capacity 1 μF, an inductance of 0.2 H and a resistance of 800 Ω are joined in series. Is
the circuit oscillatory? What is the natural frequency?

Answer 1

As per the question,

Capacity of the condenser $c=1\mu F$

Inductance $(L)=0.2H$

Resistance $(R)=800\Omega$

For the resonating frequency,

$X_L=X_c$

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

Now, substituting the values of L and C,

$\Rightarrow 2\pi f = \frac{1}{1\times 10^{-6}\times 0.2} sec^{-1}$

$\Rightarrow f=\frac{10^{7}}{2\times 2\pi } sec^{-1}$

$\Rightarrow f= 0.08\times 10^{7}sec^{-1}$

$\Rightarrow f=0.8\times 10^{6}sec^{-1}$