48 HF So we mus EXAMPLE 30-8 Damped oscillations. At t = 0, a 40-mH inductor is places in series with a resistance R 3.0

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48 Hf So We Mus Example 30 8 Damped Oscillations At T 0 A 40 Mh Inductor Is Places In Series With A Resistance R 3 0 1 (58.38 KiB) Viewed 11 times

48 HF So we mus EXAMPLE 30-8 Damped oscillations. At t = 0, a 40-mH inductor is places in series with a resistance R 3.0, and a charged capacitor c5 the time required for the charge amplitude to drop to half its starting value (a) Show that this circuit will oscillate. (b) Determine the frequency. (c) What's (d) What value of R will make the circuit nonoscillating? APPROACH We first check R2 vs. 4L/C; then use Eqs. 30-18 and 30-19 have R? < 4L/C. Since R2 = 9.002 and 4L/C = 4(0.040 H)/(4.8 x 10F) SOLUTION (a) In order to oscillate, the circuit must be underdamped, 3.3 X 10^12?, this relation is satisfied, so the circuit will oscillate. (b) We use Eq. 30-18: w 1 1 f' 3.6 X 10Hz. 2T 27 VLC (c) From Eq. 30-19, the amplitude will be half when 2 or 2L In 2 = 18 ms. R (d) To make the circuit critically damped or overdamped, we must use the criterion R? 2 4L/C = 3.3 X 10'0. Hence we must have R 2180 . R2 4L? with AC Source