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Class examples from Chapter 31

Class examples from Chapter 31 - Class examples from...

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1 Class examples from Chapter 31 11 . (a) Since the frequency of oscillation f is related to the inductance L and capacitance C by f LC 1 2 / , the smaller value of C gives the larger value of f . Consequently, max min min max 1/ 2 , 1/ 2 , f LC f LC and max max min min 365pF 6.0. 10pF C f f C (b) An additional capacitance C is chosen so the ratio of the frequencies is r 160 054 2 96 . . . . MHz MHz Since the additional capacitor is in parallel with the tuning capacitor, its capacitance adds to that of the tuning capacitor. If C is in picofarads (pF), then C C 365 10 2 96 pF pF . . The solution for C is C 365 2 96 10 2 96 1 36 2 2 pF pF pF. b g b g b g b g . . (c) We solve f LC 1 2 / for L . For the minimum frequency, C = 365 pF + 36 pF = 401 pF and f = 0.54 MHz. Thus  4 2 2 2 2 12 6 1 1 2.2 10 H. 2 2 401 10 F 0.54 10 Hz L Cf 14. The capacitors C 1 and C 2 can be used in four different ways: (1) C 1 only; (2) C 2 only; (3) C 1 and C 2 in parallel; and (4) C 1 and C 2 in series. (a) The smallest oscillation frequency is f L C C 3 1 2 2 6 2 1 2 1 2 10 10 2 0 10 60 10 b g c hc h . . . H F+5.0 10 F Hz 6 . (b) The second smallest oscillation frequency is
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2  2 1 2 6 1 1 1 7.1 10 Hz 2 2 1.0 10 H 5.0 10 F f LC . (c) The second largest oscillation frequency is  3 2 2 6 2 1 1 1.1 10 Hz 2 2 1.0 10 H 2.0 10 F f LC . (d) The largest oscillation frequency is   6 6 3 4 2 6 6 1 2 1 2 1 1 2.0 10 F+5.0 10 F 1.3 10 Hz 2 1.0 10 H 2.0 10 F 5.0 10 F 2 / f LC C C C
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