<p>An inductor of inductance 2.0 mH is connected across a charged capacitor of capacitance 5.0&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#956;</mi><mi>F</mi></math>&nbsp;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 maximum value of charge q is 200<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#956;</mi><mi>C</mi></math></p>

<p>(a) When q = 100&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#956;</mi><mi>C</mi></math>, what is the value of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfrac><mrow><mi>d</mi><mi>l</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mfenced></math>?</p>

<p>(b) When q = 200&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>&#956;</mi><mi>C</mi></math>, what is the value of I?</p>

<p>(c) Find the maximum value of I.</p>

<p>(d) When I is equal to one-half its maximum value, what is the value of&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mi>q</mi></mfenced></math>?</p>