16

CIRCUIT CONCEPTS

[CHAP. 2

Fig. 2-12 dv d ¼ 60  106 ð25:0  103 tÞ ¼ 1:5 A dt dt p ¼ vi ¼ 37:5  103 t ðWÞ ðt wC ¼ p dt ¼ 1:875  104 t2 ðmJÞ i¼C

0

See Fig. 2-13.

or

Wmax ¼ ð1:875  104 Þð2  103 Þ2 ¼ 75:0 mJ 1 1 Wmax ¼ CV2max ¼ ð60:0  106 Þð50:0Þ2 ¼ 75:0 mJ 2 2

Fig. 2-13

2.6

A 20.0-mF capacitance is linearly charged from 0 to 400 mC in 5.0 ms. Find the voltage function and Wmax . ! 400  106 q¼ t ¼ 8:0  102 t ðCÞ 5:0  103 v ¼ q=C ¼ 4:0  103 t ðVÞ Vmax ¼ ð4:0  103 Þð5:0  103 Þ ¼ 20:0 V

2.7

Wmax ¼

1 CV2max ¼ 4:0 mJ 2

A series circuit with R ¼ 2, L ¼ 2 mH, and C ¼ 500 mF has a current which increases linearly from zero to 10 A in the interval 0  t  1 ms, remains at 10 A for 1 ms  t  2 ms, and decreases linearly from 10 A at t ¼ 2 ms to zero at t ¼ 3 ms. Sketch vR , vL , and vC . vR must be a time function identical to i, with Vmax ¼ 2ð10Þ ¼ 20 V. For 0 < t < 1 ms, di ¼ 10  103 A=s dt When di=dt ¼ 0, for 1 ms < t < 2 ms, vL ¼ 0.

and

vL ¼ L

di ¼ 20 V dt

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An