Answer to Question #128073 in Classical Mechanics for Md Shajidul Sheikh Shajid

Question #128073
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?
1
Expert's answer
2020-08-02T15:12:57-0400

As per the question,

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

Inductance (L)=0.2H(L)=0.2H

Resistance (R)=800Ω(R)=800\Omega

For the resonating frequency,

XL=XcX_L=X_c

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

Now, substituting the values of L and C,

2πf=11×106×0.2sec1\Rightarrow 2\pi f = \frac{1}{1\times 10^{-6}\times 0.2} sec^{-1}


f=1072×2πsec1\Rightarrow f=\frac{10^{7}}{2\times 2\pi } sec^{-1}

f=0.08×107sec1\Rightarrow f= 0.08\times 10^{7}sec^{-1}

f=0.8×106sec1\Rightarrow f=0.8\times 10^{6}sec^{-1}


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