CHAP. 16]

THE LAPLACE TRANSFORM METHOD

417

16.30

In the circuit of Fig. 16-23, Q0 ¼4 300 mC at the time the switch is closed. transient. Ans: i ¼ 2:5e2:510 t (A)

16.31

In the circuit shown in Fig. 16-24, the capacitor has an initial charge Q0 ¼ 25 mC and the sinusoidal voltage source is v ¼ 100 sin ð1000t þ Þ (V). Find the resulting current if the switch is closed at a time corresponding to  ¼ 308. Ans: i ¼ 0:1535e4000t þ 0:0484 sin ð1000t þ 1068Þ (A)

16.32

A series RLC circuit, with R ¼ 5 , L ¼ 0:1 H, and C ¼ 500 mF, has a constant voltage V ¼ 10 V applied at t ¼ 0. Find the resulting current. Ans: i ¼ 0:72e25t sin 139t (A)

Fig. 16-24

Find the resulting current

Fig. 16-25

16.33

In the series RLC circuit of Fig. 16-25, the capacitor has an initial charge Q0 ¼ 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 ¼ 0. Ans: i ¼ e25t ð2 cos 222t  0:45 sin 222tÞ (A)

16.34

A series RLC circuit, with R ¼ 5 , L ¼ 0:2 H, and C ¼ 1 F has a voltage source v ¼ 10e100t (V) applied at t ¼ 0. Find the resulting current. Ans: i ¼ 0:666e100t þ 0:670e24:8t  0:004e0:2t (A)

16.35

A series RLC circuit, with R ¼ 200 , L ¼ 0:5 H, and C ¼ 100 mF has a sinusoidal voltage source v ¼ 300 sin ð500t þ Þ (V). Find the resulting current if the switch is closed at a time corresponding to  ¼ 308. Ans: i ¼ 0:517e341:4t  0:197e58:6t þ 0:983 sin ð500t  198Þ (A)

16.36

A series RLC circuit, with R ¼ 5 , L ¼ 0:1 H, and C ¼ 500 mF has a sinusoidal voltage source v ¼ 100 sin 250t (V). Find the resulting current if the switch is closed at t ¼ 0. Ans: i ¼ e25t ð5:42 cos 139t þ 1:89 sin 139tÞ þ 5:65 sinð250t  73:68Þ (A)

16.37

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 ¼ 2:5ð1 þ e10 t Þ ðAÞ, i2 ¼ 5e10 t (A)

Fig. 16-26

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An