Basic Circuit Theory Chpter13 Problems I If f(t)=100 for 0<t<l ms, f(t)=40 for 1 <t<2.5 ms, f(t)=0 for 2.5<t<10 ms, where T 10 ms, find As and A-5 2 Complex Fourier coefficients for a certain periodic voltage are: A=10, A=8-j6, A2=5+j0, A3=1+j2, A4=1+j0, and Am=0 for n>4.(a) Calculate v at t=T/4.(b) Find the average power delivered by this waveform to a 5Q2 resistor 3 Let v(t)=3-3 cos(100 t-40)+4 sin(200 T t-10)+2.5 cos 300 tt V Find: (a)the average value Var;(b)the rms value V;(c)the period T; (d)v(18ms) 4 The waveform shown in Fig. 13-12 is periodic with T=1Os. Find(a) the average value,(b)the ue;(c)the value of a3 ↑f() f(1) 2 t (s) Fig.13-12F 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 6 Find i(t) in the circuit of Fig. 13-14 given that s(=1+∑ 3nt A 2 2H 10mF=V (b) Fig.13-15F 7 7 The periodic voltage waveform in Fig. 13-15a is applied to the circuit in Fig. 13-15b. Find the age vo(t) across the capac 8 The volt the terminals of a circuit is DaLian Maritime UniversityBasic 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, A1=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 Ω 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 . a3 4 t (s) 2 5 f (t ) − 5 2 − 2 0 − 0 6 2 4 t 4 f (t) −6 −4 2 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 cos3 1 1 ∑ 2 ∞ = A (t) 2 Ω i 2H 1Ω s i (a) (b) Fig. 13-15 For prob. 7. - + - + 1 s v 20Ω t 10mF − 1 10 − 2 o v 0 2 3 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