418

16.38

THE LAPLACE TRANSFORM METHOD

[CHAP. 16

For the two-mesh network shown in Fig. 16-27, ﬁnd the currents i1 and i2 which result when the switch is closed at t ¼ 0. Ans: i1 ¼ 0:101e100t þ 9:899e9950t (A), i2 ¼ 5:05e100t þ 5 þ 0:05e9950t (A)

Fig. 16-27

16.39

In the network shown in Fig. 16-28, the 100-V source passes a continuous current in the ﬁrst loop while the switch is open. Find the currents after the switch is closed at t ¼ 0. Ans: i1 ¼ 1:67e6:67t þ 5 (A), i2 ¼ 0:555e6:67t þ 5 (A)

16.40

The two-mesh network shown in Fig. 16-29 contains a sinusoidal voltage source v ¼ 100 sin ð200t þ Þ (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 ¼ 3:01e100t þ 8:96 sin ð200t  63:48Þ (A), i2 ¼ 1:505e100t þ 4:48 sin ð200t  63:48Þ (A)

Fig. 16-28

16.41

Fig. 16-29

In the circuit of Fig. 16-30, vð0Þ ¼ 1:2 V and ið0Þ ¼ 0:4 A. Ans:

Find v and i for t > 0.

v ¼ 1:3334et  0:1334e2:5t ; t > 0 i ¼ 0:66667et  0:2667e2:5t ; t > 0

Fig. 16-30

16.42

In the circuit of Fig. 16-31, ig ðtÞ ¼ cos tuðtÞ. Ans:

v ¼ 0:8305 cos ðt  48:48Þ; t > 0 i ¼ 0:2626 cos ðt  66:88Þ; t > 0

Fig. 16-31

Find v and i.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An