14. A periodic (but not harmonic) electromotive force ECt) Eo(1 4t/T) (0 S t T/2

Question

14. A periodic (but not harmonic) electromotive force ECt) Eo(1 4t/T) (0 S t T/2) [with E(t T) E(t)] is applied to the LRC-circuit in Fig. 4.7. a) Develop the solution for the current I(t) in the following Fourier Series form: I(t) co cn sin (nut opn), n 1 where w 2T/T; note the use of sine functions. b) Let R 1.62, L 6.35 mh, c P 4 uf, Eo 12 V, an T 5 x 10-3 Sec. Prepare your expressions for cn and tan pn for rapid numerical calculation, and calculate cn and tan pn up to n 13 c Explain the physical reason why the amplitude c5 dominates all the others. Comment on the behavior of on.

Explanation / Answer

c.) the fifth harmonic dominates as in the series RLC ckt., fifth harmonic frequency i.e. (20/T) is equal to the resonant frequency of the ckt. i.e. w=1/sqrt(LC).

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