Q

An LC circuit contains a 20 mH inductor and a 50 μF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.What is the total energy stored initially

Q7.12  (a) An $LC$ circuit contains a $20mH$ inductor and a $50\mu F$ capacitor with an initial charge of $10mC$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$.

What is the total energy stored initially? Is it conserved during $LC$ oscillations?

Views

Given,

The inductance of the inductor:

$L=20mH=20*10^{-3}H$

The capacitance of the capacitor :

$C=50\mu F=50*10^{-6}F$

The initial charge on the capacitor:

$Q=10mC=10*10^{-3}C$

Total energy present at the initial moment:

$E_{initial}=\frac{Q^2}{2C}=\frac{(10*10^{-3})^2}{2*50*10^{-6}}=1J$

Hence initial energy in the circuit is 1J. Since we don't have any power-consuming element like  resistance in the circuit, the energy will be conserved

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