Basic Circuit Theory Chpter13 Problems 1 If f(t) = 100 for 0 < t < 1 ms, f(t) = 40 for 1 < t < 2.5 ms, f(t) = 0 for 2.5 < t < 10 ms, where T = 10 ms, find A and A . 5 5? 2 Complex Fourier coefficients for a certain periodic voltage are: A =10, A 1 =8-j6, A =5+j0, A 3 =1+j2, A =1+j0, and A =0 for n > 4. (a) Calculate v at t=T/4. (b) Find the average power delivered by this waveform to a 5 resistor. 0 2 4 n ? 3 Let v(t) = 3 – 3 cos (100π t - 40 o )+4 sin(200π t - 10 )+2.5 cos 300 o π t V. Find: (a) the average value V ; (b) the rms value V; (c) the period T; (d) v(18ms). av 4 The waveform shown in Fig. 13-12 is periodic with T=10s. Find (a) the average value; (b) the effective value; (c) the value of . 3 a 4 t )s( 52 )(tf 5? 2 02? 4 ? 2 t06 4 )(tf 4 26 ? ? Fig. 13-12 For prob. 4. Fig. 13-13 For prob. 5. 5 Find the Fourier series for the signal in Fig. 13-13. Evaluate f(t) at t=2 using the first three nonzero harmonics. 6 Find i(t) in the circuit of Fig. 13-14 given that i S (t) = 1 + nt n n 3cos 1 1 2 ∑ ∞ = A )(t ?2 i H2 ?1 s i (a) (b) Fig. 13-15 For prob. 7. - + - + 1 s v ?20 t mF10 1? 10 2? o v 230 s v Fig. 13-14 For prob. 6. 7 The periodic voltage waveform in Fig. 13-15a is applied to the circuit in Fig. 13-15b. Find the voltage v (t) across the capacitor. 0 8 The voltage across the terminals of a circuit is DaLian Maritime University 1 Basic Circuit Theory Chpter13 Problems v(t) = 30 + 20 cos(60π t+45 ) + 10 cos(60 o π t-45 o ) V If the current entering the terminal at higher potential is i(t) = 6 + 4 cos(60π t+10 o ) - 2 cos(120π t-60 ) A o find: (a) the rms value of the voltage and the current, (b) The average power absorbed by the circuit. 9 Consider the periodic signal in Fig. 13-16. (a) Find the actual rms value of f(t). (b) Use the first five nonzero harmonics of the Fourier series to obtain an estimate for the rms value. 10 For the circuit in Fig. 13-17 i(t) = 20 + 16 cos(10t+45 o ) + 12 cos(20t-60 ) mA o find v(t), and calculate the average power dissipated in the resistor. - +)(ti v F100μ ?k2 )(t 3 t041?3? 5 2 )(tf 15? 2 Fig. 13-16 For prob. 9. Fig. 13-17 For prob. 10. Reference Answers to Selected Problems 1: A =5.25 , A =5.25 . 5 o 0.76?∠ 5? o 0.76∠ 2: (a) 18V; (b) 72.4W. 3: (a) 3.00V; (b) 4.96V; (c) 0.02s; (d) –2.46V. 4: (a) 1.200; (b) 1.932; (c) –0.0458. 5: 2+ 3 cos) 3 cos 3 2 (cos 124 1 22 tnnn n n πππ π ? ∑ ∞ = , 3.756 6: )2tan3cos( 413 1 3 1 1 1 22 nn nnn ? ∞ = ? + + ∑ A. 7: ∑ ∞ = ? + +? 1 22 1 25 )/5tan90sin(100 k nn ntn π ππ π o V, n=2k-1. 8: (a) 33.91V; (b) 6.782 A; (c) 203.1W. 9: (a) 1.155; (b) 0.8162. 10: (a) 40 + 0.01431 cos (10t-18.43 o )+ 0.05821 cos (20t -136 )V; o (b) 800 mW. DaLian Maritime University 2