An inductor of inductance `2.0 mH` s connected across a charged capacitor of capacitance `5.0 mu F` and the resulting `LC` circuit is set oscillating at its natural frequency. Let `Q` denote the instantaneous charge on the capacitor and `I` the current in the circuit. It is found that the maximum value of charge `Q` is `200 mu C`. a. When `Q = 100 mu C`, what is the value of `|(dI)/(dt)|`? b. When `Q = 200 mu C`, what is the value of `I`? c. Find the maximum value of `I`. d. When `I` is equal to one-half its maximum value, what is the value of `|Q|`?

An inductor of inductance `2.0 mH` s connected across a charged capaci

1.	An inductor of inductance `2.0 mH` s connected across a charged capacitor of capacitance `5.0 mu F` and the resulting `LC` circuit is set oscillating at its natural frequency. Let `Q` denote the instantaneous charge on the capacitor and `I` the current in the circuit. It is found that the maximum value of charge `Q` is `200 mu C`. a. When `Q = 100 mu C`, what is the value of `\|(dI)/(dt)\|`? b. When `Q = 200 mu C`, what is the value of `I`? c. Find the maximum value of `I`. d. When `I` is equal to one-half its maximum value, what is the value of `\|Q\|`?
Answer» Correct Answer - `(a) 10^(4) A//s (b) 0 (c ) 2A (d) 100sqrt(3)muC` Given that `Q=Q_(0) cosomegat` `omega=1/sqrt(LC)=1/sqrt(2xx10^(-3)xx5xx10^(-6))=10^(4) rad//sec` `(a) Q=Q_(0) cosomegat implies 100=200 cosomegat` `cosomegat=1/2` `since Q=Q_(0) cosomegat implies I=(dQ)/(dt)=Q_(0) omega sinomegat` `(dI)/(dt)=-Q_(0)omega^(2) cosomegat` `\|(dI)/(dt)\|=omega^(2)(Q_(0)cosomegat)=omega^(2)Q=10^(8)xx100xx10^(-6)` `10^(4) Amp//sec` `(b) Q=Q_(0)cosomegat` `200=200 cosomegat implies cosomegat=1` `sinomegat=0` `I=(dQ)/(dt)=-Q_(0)omega sin omegat=0` `(c ) l_(max)=Q_(0)omega=200xx10^(-6)xx10^(4)=2Amp` `(d) I=-I_(0) sinomegat` `I_(0)/2=-I_(0)sinomegat` `sinomegat=sin (7pi)/6 implies omegat=(7pi)/6` `cosomegat=cos(7pi)/6=-cospi/6=-(-sqrt(3))/2` `Q=Q_(0)cosomegat=200muCxx(-sqrt(3)/2)` `=-100sqrt(3)muC` `\|Q\|=100sqrt(3) muC`

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