homework1.pdf - 9.3 Consider the sinusoidal voltage ’00 =...

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Unformatted text preview: 9.3 Consider the sinusoidal voltage ’00) = 25 cos (40017: + 60°) V. a) What is the maximum amplitude of the voltage? b) What is the frequency in hertz? c) What is the frequency in radians per second? d) What is the phase angle in radians? e) What is the phase angle in degrees? f) What is the period in milliseconds? g) What is the first time after t = 0 that v = 0 V? h) The sinusoidal function is shifted 5/ 6 ms to the right along the time axis. What is the expression for '00:)? i) What is the minimum number of milliseconds that the function must be shifted to the left if the expression for v(t) is 25 sin 40017: V? 9.9 The voltage applied to the circuit shown in Fig. 9.5 at r = 0 is 75 cos (4000f — 60°) V. The circuit resist- ance is 400 (I and the initial current in the 75 mH inductor is zero. a) Find EU) fort 3-: 0. 13) Write the expressions for the transient and steady-state components of i(r). c) Find the numerical value off after the switch has been closed for 750 as. d) What are the maximum amplitude, frequency (in radians per second), and phase angle of the steady-state current? e) By how many degrees are the voltage and the steady-state current out of phase? 9.]1 Use the concept of the phasor to combine the fol- lowing sinusoidal functions into a single trigono- metric expression: a) y = 30 cos(200r — 160°) + 15 cos(200r + 70°), b) y = 90 sin(50r — 20°) + 60 cos(200t - 70°), c) y = 50 cos(5000t — 60°) + 25 8111(50001‘ + 110°) — 75 cos(5000i‘ - 30°), d) y = 10 cos (wt + 30°) + 10 sin wt + 10 cos(wt + 150°). 9.14 The expressions for the steady-state voltage and current at the terminals of the circuit seen in Fig. P914 are '08, = 300 cos (500017: + 78°) V, i, = 65111 (500011"! + 123°) A a) What is the impedance seen by the source? b) By how many microseconds is the current out of phase with the voltage? 9.16 A 25 D. resistor and a 10 mI-I inductor are con- PSPIEE nected in parallel. This parallel combination is also mum“ in parallel with the series combination of a 30 .0. resistor and a 10 n13 capacitor. These three parallel branches are driven by a sinusoidal current source whose current is 125 sin(2500t + 60°) A. a) Draw the frequency-domain equivalent circuit. b) Reference the voltage across the current source as a rise in the direction of the source current, and find the phasor voltage. c) Find the steady-state expression for v(t). 9.20 a) Show that at a given frequency w, the circuits in Fig. P9.20(a) and (b) will have the same imped- ance between the terminals a,b if R2 R1: 2 2 a 1+wR2C2 C _ 1 + (0212365 1— . w2R%C2 b) Find the values of resistance and capacitance that when connected in series will have the same impedance at 40 krad/s as that of a 10000. resistor connected in parallel with a 50 nF capacitor. Figure P9.20 a a R1 R2 C2 C1 1 b (a) (b) 9.23 Find the admittance Yab in the circuit seen in Fig. P923. Express Yab in both polar and rectangu- lar form. Give the value of Yab in millisiemens. Figure P923 —j12.8 D. 1'10 .0 9.32 Find lb and Z in the circuit shown in Fig. P932 if Vg = 25£°Vandla = 5 {90° A. Figure P9.3 2 9.34 Find the steady-state expression for '00 in the circuit of Fig. P934 if £3, = 60 cos 10,000t mA. Figure P934 son ZuF 10 mH 100 D. ...
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