14

CIRCUIT CONCEPTS

[CHAP. 2

V 0:74  ¼ 25:78  I 28:7  103 V 0:75  0:73  ¼ 0:85  r¼ I ð42:7  19:2Þ  103

p ¼ VI  0:74  28:7  103 W ¼ 21:238 mW EXAMPLE 2.5. The current and voltage characteristic of a tungsten ﬁlament light bulb is measured and recorded in the following table. Voltages are DC steady-state values, applied for a long enough time for the lamp to reach thermal equilibrium.

v (V)

0.5

1

1.5

2

3

3.5

4

4.5

5

5.5

6

6.5

7

7.5

8

i (mA)

4

6

8

9

11

12

13

14

15

16

17

18

18

19

20

Find the static and dynamic resistances of the ﬁlament and also the power consumption at the operating points (a) i ¼ 10 mA; (b) i ¼ 15 mA. R¼

V ; I

V ; I

p ¼ VI

ðaÞ

R

2:5 32 ¼ 250 ; r  ¼ 500 ; p  2:5  10  103 W ¼ 25 mW 10  103 ð11  9Þ  103

ðbÞ

R

5 5:5  4:5 ¼ 333 ; r  ¼ 500 ; p  5  15  103 W ¼ 75 mW 15  103 ð16  14Þ  103

Solved Problems 2.1

A 25.0- resistance has a voltage v ¼ 150:0 sin 377t (V). Find the corresponding current i and power p. i¼

2.2

v ¼ 6:0 sin 377t ðAÞ R

p ¼ vi ¼ 900:0 sin2 377t ðWÞ

The current in a 5- resistor increases linearly from zero to 10 A in 2 ms. At t ¼ 2þ ms the current is again zero, and it increases linearly to 10 A at t ¼ 4 ms. This pattern repeats each 2 ms. Sketch the corresponding v. Since v ¼ Ri, the maximum voltage must be ð5Þð10Þ ¼ 50 V. In Fig. 2-10 the plots of i and v are shown. The identical nature of the functions is evident.

2.3

An inductance of 2.0 mH has a current i ¼ 5:0ð1  e5000t Þ (A). Find the corresponding voltage and the maximum stored energy. v¼L

di ¼ 50:0e5000t ðVÞ dt

In Fig. 2-11 the plots of i and v are given. Since the maximum current is 5.0 A, the maximum stored energy is Wmax ¼

1 2 ¼ 25:0 mJ LI 2 max

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An