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An LC circuit contains a 20 mH inductor and a 50 muF capacitor with an initial charge of 10 mC. The resistance of 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 ? |
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Answer» Solution :(a) 1.0 J. Yes, SUM of the ENERGIES stored in L and C is conserved if R = 0. (b) `omega=10^(3)rad s^(-1), v=159Hz` (c ) `q=q_(0)cosomega t` (i) Energy stored is completely electrical at `t=0, (T)/(2), T, (3T)/(2), ……` (ii) Energy stored is completely magnetic (i.e., electrical energy is zero) at `t=(T)/(4), (3T)/(4), (5T)/(4).......`, where `T=(1)/(v)=6.3ms`. (d) At `(T)/(8), (3T)/(8), (5T)/(8) ..........`, because `q=q_(0)"cos"(OMEGAT)/(8) =q_(0)"cos"(pi)/(4)=(q_(0))/(sqrt(2))`. Therefore, electrical energy `=(q^(2))/(2C)=(1)/(2)((q_(0)^(2))/(2C))` which is half the total energy. R damps out the LC oscillations eventually. The whole of the initial energy (= 1.0 J) is eventually dissipated as heat. |
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