Lecture-17Examples-03-12-08

Lecture-17Examples-03-12-08 - Lecture-17 Examples...

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Lecture-17 Examples HW-17-5. (HRW 31-20) An oscillating LC circuit has a current amplitude of 7.50 mA, a potential amplitude of 250 mV, and a capacitance of 220 nF. What are (a) the period of oscillation, (b) the maximum energy stored in the capacitor, (c) the maximum energy stored in the inductor, (d) the maximum rate at which the current changes, and (e) the maximum rate at which the inductor gains energy? Solution: 20. (a) From V = IX C we find ω = I/CV . The period is then T = 2 π / ω = 2 π CV/I = 46.1 μ s. (b) The maximum energy stored in the capacitor is 27 2 9 11 (2.20 10 F)(0.250 V) 6.88 10 J 22 E UC V −− == × = × . (c) The maximum energy stored in the inductor is also 2 /2 B UL I = = 6.88 nJ . (d) We apply Eq. 30-35 as V = L ( di/dt ) max . We can substitute L = CV 2 /I 2 (combining what we found in part (a) with Eq. 31-4) into Eq. 30-35 (as written above) and solve for ( di/dt ) max . Our result is 23 2 3 7 max (7.50 10 A) 1.02 10 A/s / (2.20 10 F)(0.250 V) di V V I dt L CV I CV × ⎛⎞ = = = × ⎜⎟ × ⎝⎠ .
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Lecture-17Examples-03-12-08 - Lecture-17 Examples...

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