7.8 Suppose the initial charge on the capacitor in Exercise 7.7 is 6 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?
Total energy stored in the capacitor can be calculated as:
E = == 0.6 J
Total energy at a later time will remain same because energy is shared between the capacitor and the inductor.
<p><strong>7.8 </strong>Capacitance of the capacitor, C = 30<span title="Click to copy mathml"><math><mi>μ</mi><mi>F</mi></math></span> = 30<span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>6</mn></mrow></mrow></msup></math></span> F</p><p>Inductance of the Inductor, L = 27 mH = 27<span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>3</mn></mrow></mrow></msup></math></span> H</p><p>Charge on the capacitor, Q = 6 mC= 6<span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>3</mn></mrow></mrow></msup></math></span> C</p><p>Total energy stored in the capacitor can be calculated as:</p><p>E =<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac><mfrac><mrow><mrow><msup><mrow><mrow><mi>Q</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mi>C</mi></mrow></mrow></mfrac></math></span> =<span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1</mn></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></mfrac><mfrac><mrow><mrow><mo>(</mo><msup><mrow><mrow><mn>6</mn><mi mathvariant="normal"></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>3</mn></mrow></mrow></msup><mo>)</mo></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>30</mn><mi mathvariant="normal"></mi><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>6</mn></mrow></mrow></msup></mrow></mrow></mfrac></math></span>= 0.6 J</p><p>Total energy at a later time will remain same because energy is shared between the capacitor and the inductor.</p>
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