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 , ? , and A if f(t) = A sin(ω t + ? ); (b) find θ , A, and f(0.0014) if f(t) = 5cos(ω t + θ ). 0 t )(tf 8 2.1 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). ? S + - + - i R v s v R L Fig. 7-12 For prob.3. 4 A 0.25H inductor having a wire resistance of 10? 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 ? ? combination). 5 Give in polar form for: (a) 20∠ 110 - 8 o ∠ 40 , (b) o )541.017.1( )82.31.6( j j + ? . Give in rectangular form for: (c) 71.93.6 j j ? , (d) e . o 521.2 ∠j 6 (a) The complex current, 8e A, is applied to the series combination of a 12 )60200( o ?tj ? 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 )15010000( o +tj ? 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 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 H1 ?100 F40μ RI ? 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. F1 in Z R L R in Y Fig. 7-14 For prob.10. DaLian Maritime University 2 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 5.133∠ o 9.56?∠ 6: (a) 101.2e V; (b) 0.67e A. )6.41200( o ?tj o 6.14610( ?tj 7: (a) 7.81 ; (b) 3.0 ; (c) 6.36 . o 8.39∠ o 3.56?∠ o 6.7∠ 8: (a) 95.8 2 cos(ω t+94 ) mA; (b) 25.1 mA. o o 6.111?∠ 9: (a) 11.6 mA; (b) 1.71 mA. o 11?∠ o 1∠ 10: 1 , 1H. ? DaLian Maritime University 3