how to generate barcode in ssrs report THE LAPLACE TRANSFORM METHOD in Software

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THE LAPLACE TRANSFORM METHOD
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In the circuit of Fig. 16-23, Q0 4 300 mC at the time the switch is closed. transient. Ans: i 2:5e 2:5 10 t (A)
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Find the resulting current
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In the circuit shown in Fig. 16-24, the capacitor has an initial charge Q0 25 mC and the sinusoidal voltage source is v 100 sin 1000t  (V). Find the resulting current if the switch is closed at a time corresponding to  308. Ans: i 0:1535e 4000t 0:0484 sin 1000t 1068 (A) A series RLC circuit, with R 5
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, L 0:1 H, and C 500 mF, has a constant voltage V 10 V applied at t 0. Find the resulting current. Ans: i 0:72e 25t sin 139t (A)
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Fig. 16-24
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Fig. 16-25
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In the series RLC circuit of Fig. 16-25, the capacitor has an initial charge Q0 1 mC and the switch is in position 1 long enough to establish the steady state. Find the transient current which results when the switch is moved from position 1 to 2 at t 0. Ans: i e 25t 2 cos 222t 0:45 sin 222t (A) A series RLC circuit, with R 5
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, L 0:2 H, and C 1 F has a voltage source v 10e 100t (V) applied at t 0. Find the resulting current. Ans: i 0:666e 100t 0:670e 24:8t 0:004e 0:2t (A)
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A series RLC circuit, with R 200
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, L 0:5 H, and C 100 mF has a sinusoidal voltage source v 300 sin 500t  (V). Find the resulting current if the switch is closed at a time corresponding to  308. Ans: i 0:517e 341:4t 0:197e 58:6t 0:983 sin 500t 198 (A)
A series RLC circuit, with R 5
, L 0:1 H, and C 500 mF has a sinusoidal voltage source v 100 sin 250t (V). Find the resulting current if the switch is closed at t 0. Ans: i e 25t 5:42 cos 139t 1:89 sin 139t 5:65 sin 250t 73:68 (A)
In the two-mesh network of Fig. 16-26, the currents are selected as shown in the diagram. Write the timedomain equations, transform them5 into the corresponding s-domain equations, and obtain the currents i1 5 and i2 . Ans: i1 2:5 1 e 10 t A , i2 5e 10 t (A)
Fig. 16-26
THE LAPLACE TRANSFORM METHOD
[CHAP. 16
For the two-mesh network shown in Fig. 16-27, nd the currents i1 and i2 which result when the switch is closed at t 0. Ans: i1 0:101e 100t 9:899e 9950t (A), i2 5:05e 100t 5 0:05e 9950t (A)
Fig. 16-27
In the network shown in Fig. 16-28, the 100-V source passes a continuous current in the rst loop while the switch is open. Find the currents after the switch is closed at t 0. Ans: i1 1:67e 6:67t 5 (A), i2 0:555e 6:67t 5 (A) The two-mesh network shown in Fig. 16-29 contains a sinusoidal voltage source v 100 sin 200t  (V). The switch is closed at an instant when the voltage is increasing at its maximum rate. Find the resulting mesh currents, with directions as shown in the diagram. Ans: i1 3:01e 100t 8:96 sin 200t 63:48 (A), i2 1:505e 100t 4:48 sin 200t 63:48 (A)
Fig. 16-28
Fig. 16-29
In the circuit of Fig. 16-30, v 0 1:2 V and i 0 0:4 A. Ans: v 1:3334e t 0:1334e 2:5t ; t > 0 i 0:66667e t 0:2667e 2:5t ; t > 0
Find v and i for t > 0.
Fig. 16-30
Fig. 16-31
In the circuit of Fig. 16-31, ig t cos tu t . Ans: v 0:8305 cos t 48:48 ; t > 0 i 0:2626 cos t 66:88 ; t > 0
Find v and i.
CHAP. 16]
THE LAPLACE TRANSFORM METHOD  1A cos t
In the circuit of Fig. 16-31, ig 16.41 and 16.42. Ans:
t<0 . Find v and i for t > 0 and compare with results of Problems t>0
v 0:6667e t 0:0185e 2:5t 0:8305 cos t 48:48 ; t > 0 i 0:3332e t 0:0368e 2:5t 0:2626 cos t 66:88 ; t > 0
Find capacitor voltage v t in the circuit shown in Fig. 16-32. Ans: v 20 10:21e 4t cos 4:9t 11:538 ; t > 0
Fig. 16-32
Find inductor current i t in the circuit shown in Fig. 16-32. Ans: i 10 6:45e 4t cos 4:9t 39:28 ; t > 0
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