Basic circuit the Chpter7 Problems I A cosine voltage is zero and increasing at t=-1 6ms; the next zero crossing occurs at t 4.65ms. (a)Calculate T, f, and @.(b) If v(0)=20V, find v(t).(c)By what angle does v(t) I(t)=5cos(t-110°)A? 2 For the sinusoidal waveform shown in Fig. 7-11, (a)find T, f, @, and A if f(t)=Asin(@t P ); (b)find 6, A, and f(0.0014)if f(t)=5cos(ot+ 0) f(1) Fig. 7-11 For prob. 2 3 With reference to the circuit of Fig 7-12 let i= 2sin(500t-40)A,R=200 Q2, and L=0.1H Determine the source voltage vs(t) Fig. 7-12 For prob. 3 4 A025H inductor having a wire resistance of 10Q2 is connected to a 50 Hz source. If the open-circuit source-voltage amplitude is 120 2 V and its internal resistance is 2Q2, find the amplitude of the sinusoidal voltage across the inductor(0.25H and 10Q2 combination) 5 Give in polar form for: (a)204. 8240,(b) -(6. 1-j3 82). Give in rectangular (1.17+0.541) form for: (c) 63-/97(d)e2l∠2 6(a)The complex current, 8e /(2007-60)A, is applied to the series combination of a 1292 resistor and a 20mH inductor. Assuming the passive sign convention, find the complex voltage across the combination.(b)The complex voltage, 60e /1000 +50 )v, is applied to the parallel combination of a 200 Q2 resistor and a 1 u F capacitor. Assuming the passive sig convention, find the complex current entering the parallel combination. 7 Express the single phasor in polar form that is equavilent to cos200-5√2sin200t DaLian Maritime University
Basic Circuit Theory Chpter7 Problems 1 A cosine voltage is zero and increasing at t = - 1.6ms; the next zero crossing occurs at t = 4.65ms. (a) Calculate T, f, and ω . (b) If v(0) = 20V, find v(t). (c) By what angle does v(t) lead the current i(t) = 5cos(ω t - 110 o ) A? 2 For the sinusoidal waveform shown in Fig.7-11, (a) find T, f, ω , ϕ , and A if f(t) = A sin(ω t + ϕ ); (b) find θ , A, and f(0.0014) if f(t) = 5cos(ω t + θ ). 0 t f (t) 8 1.2 − 8 − 5 (ms) Fig. 7-11 For prob.2. 3 With reference to the circuit of Fig.7-12 let i = 2sin(500t - 40 o ) A, R = 200 , and L = 0.1H. Determine the source voltage v (t). Ω S + - + - i R v s v R L Fig. 7-12 For prob.3. 4 A 0.25H inductor having a wire resistance of 10Ω is connected to a 50 Hz source. If the open-circuit source-voltage amplitude is 120 2 V and its internal resistance is 2 , find the amplitude of the sinusoidal voltage across the inductor (0.25H and 10 Ω Ω combination). 5 Give in polar form for: (a) 20∠ 110 - 8 o ∠ 40 , (b) o (1.17 0.541) (6.1 3.82) j j + − . Give in rectangular form for: (c) 6.3 j9.71 j − , (d) e . o j 2.1∠52 6 (a) The complex current, 8e A, is applied to the series combination of a 12 (200 60 )o j t− Ω resistor and a 20mH inductor. Assuming the passive sign convention, find the complex voltage across the combination. (b) The complex voltage, 60e V, is applied to the parallel combination of a 200 resistor and a 1 (10000 150 )o j t+ Ω µ F capacitor. Assuming the passive sign convention, find the complex current entering the parallel combination. 7 Express the single phasor in polar form that is equavilent to: (a) 2 cos200t - 5 2 sin200t; DaLian Maritime University 1
Basic Circuit Theory Chpter7 problems (b)6√2cos20t-5√2sin(200t+120°) (c)√2coot-40°)+5√2cos(ot+70°) 8 Assume that only three currents, i, i2, and i3, enter a certain node (a)Find i, (t)if 12= 65∠10° ma and3=45∠50°mA(b) Find2ifi()=552co400+40°)mA andi3()=35√2sin(400t-70°)mA 9 The network of Fig 7-13 operates at @=100 rad/s (a)If IR=0.01 A, find 1,,(b)If I1=2∠-30°A,fnd 40HF 100g Fig. 7-13 For prob. 9 10 If the input admittance and impedance of the network shown in Fig. 7-14 are equal at every frequency, find R and L R L Z IF Fig. 7-14 For prob. 10 DaLian Maritime University
Basic Circuit Theory Chpter7 Problems (b) 6 2 cos200t - 5 2 sin(200t + 120 o ); (c) 2 cos(ω t - 40 o ) + 5 2 cos(ω t + 70 ) o 8 Assume that only three currents, i 1 , i , and i , enter a certain node. (a) Find i 1 (t) if = 65 -110 mA and = 45∠ -50 o mA. (b) Find if i 1 (t) =55 2 3 • 2 I ∠ o • 3 I • 2 I 2 cos(400t+40 o ) mA and i (t) =35 3 2 sin(400t - 70 ) mA. o 9 The network of Fig.7-13 operates at ω =100 rad/s. (a) If = 0.01 • R I ∠ 20 o A, find , (b) If = 2 -30 A, find . • 1 I • 1 I ∠ o • R I 1H 40µF 100Ω I R • 1 • I Fig. 7-13 For prob.9. 10 If the input admittance and impedance of the network shown in Fig.7-14 are equal at every frequency, find R and L. 1F Zin R L R Yin Fig. 7-14 For prob.10. DaLian Maritime University 2
Basic Circuit Theory Chpter7 problems Reference answers to Selected Problems l:(a)12.5ms,80Hz,503rad/s,(b)278cos(160x-43.9)V;(c)66.1 2(a)117ms,(b)895Hz;(c)563rad/s;(d)-38.7°,8.0,(e)-1287,8.0;(f)0898 3:vs(t=412cos(500t116°)V 4:169.3V 5:(a)18.83∠1335°;(b)5.58∠-56.9°;(c)-00725+j0.047;(d0.0524+j0.1838 6:(a)1012e120=46v;b)0.67e06 7:(a)7.81∠39.8°;(b)3.0∠-563°;(c)6.36∠7.6 8:(a)958√2cos(ot94°)mA;(b)251∠-1116°mA 9(a)116∠-11°mA,(b)1.71∠1°mA 10:1g,1H DaLian Maritime University
Basic Circuit Theory Chpter7 Problems Reference Answers to Selected Problems 1: (a) 12.5 ms, 80 Hz, 503 rad/s; (b) 27.8 cos(160π -43.9 o )V; (c) 66.1 . o 2: (a) 11.17 ms; (b) 89.5 Hz; (c) 563 rad/s; (d) –38.7 o , 8.0; (e) –128.7, 8.0; (f) 0.898. 3: v (t)=412 cos(500t-116 ) V. 4: 169.3 V. S o 5: (a) 18.83 ; (b) 5.58 ; (c) – 0.0725 + j 0.047; (d)0.0524+j0.1838. o ∠133.5 o ∠ − 56.9 6: (a) 101.2e V; (b) 0.67e A. (200 41.6 )o j t− o j(10t−146.6 7: (a) 7.81 ; (b) 3.0 ; (c) 6.36 . o ∠39.8 o ∠ − 56.3 o ∠7.6 8: (a) 95.8 2 cos(ω t+94 ) mA; (b) 25.1 mA. o o ∠ −111.6 9: (a) 11.6 mA; (b) 1.71 mA. o ∠ −11 o ∠1 10: 1Ω , 1H. DaLian Maritime University 3
