Page 25 - Schaum's Outline of Theory and Problems of Electric Circuits

14
V CIRCUIT CONCEPTS [CHAP. 2
0:74
R ¼ ¼ 25:78
I 28:7 10 3
V 0:75 0:73
r ¼ ¼ 0:85
I ð42:7 19:2Þ 10 3
3
p ¼ VI 0:74 28:7 10 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.
V V
R ¼ ; r ¼ ; p ¼ VI
I I
2:5 3 2 3
ðaÞ R ¼ 250
; r ¼ 500
; p 2:5 10 10 W ¼ 25 mW
10 10 3 ð11 9Þ 10 3
5 5:5 4:5
ðbÞ R 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.
v
2
i ¼ ¼ 6:0 sin 377t ðAÞ p ¼ vi ¼ 900:0 sin 377t ðWÞ
R
þ
2.2 The current in a 5-
resistor increases linearly from zero to 10 A in 2 ms. At t ¼ 2 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 ð5Þð10Þ¼ 50 V. In Fig. 2-10 the plots of i and v are shown.
The identical nature of the functions is evident.

5000t
2.3 An inductance of 2.0 mH has a current i ¼ 5:0ð1 e Þ (A). Find the corresponding voltage
and the maximum stored energy.
di
v ¼ L 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
1 2
W max ¼ LI max ¼ 25:0mJ
2