ssrs barcodelib CIRCUIT CONCEPTS in Software

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CIRCUIT CONCEPTS
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are shown as two junctions in (b). However, resistor R4 is bypassed by a short circuit and may be removed for purposes of analysis. Then, in Fig. 2-9(c) the single junction A is shown with its three meeting branches.
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Fig. 2-9
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NONLINEAR RESISTORS
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The current-voltage relationship in an element may be instantaneous but not necessarily linear. The element is then modeled as a nonlinear resistor. An example is a lament lamp which at higher voltages draws proportionally less current. Another important electrical device modeled as a nonlinear resistor is a diode. A diode is a two-terminal device that, roughly speaking, conducts electric current in one direction (from anode to cathode, called forward-biased) much better than the opposite direction (reverse-biased). The circuit symbol for the diode and an example of its current-voltage characteristic are shown in Fig. 2-25. The arrow is from the anode to the cathode and indicates the forward direction i > 0 . A small positive voltage at the diode s terminal biases the diode in the forward direction and can produce a large current. A negative voltage biases the diode in the reverse direction and produces little current even at large voltage values. An ideal diode is a circuit model which works like a perfect switch. See Fig. 2-26. Its i; v characteristic is & v 0 when i ! 0 i 0 when v 0 The static resistance of a nonlinear resistor operating at I; V is R V=I. Its dynamic resistance is r V= I which is the inverse of the slope of the current plotted versus voltage. Static and dynamic resistances both depend on the operating point.
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EXAMPLE 2.4. The current and voltage characteristic of a semiconductor diode in the forward direction is measured and recorded in the following table: v (V) i (mA) 0.5 2 10
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0.6 0.11
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0.65 0.78
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0.66 1.2
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0.68 2.6
0.69 3.9
0.70 5.8
0.71 8.6
0.72 12.9
0.73 19.2
0.74 28.7
0.75 42.7
In the reverse direction (i.e., when v < 0), i 4 10 15 A. Using the values given in the table, calculate the static and dynamic resistances (R and r) of the diode when it operates at 30 mA, and nd its power consumption p. From the table
CIRCUIT CONCEPTS
[CHAP. 2
V 0:74 % 25:78  I 28:7 10 3 V 0:75 0:73 % 0:85  r I 42:7 19:2 10 3
p VI % 0:74 28:7 10 3 W 21:238 mW
EXAMPLE 2.5. The current and voltage characteristic of a tungsten lament 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) i (mA)
0.5 4
1.5 8
3 11
3.5 12
4 13
4.5 14
5 15
5.5 16
6 17
6.5 18
7 18
7.5 19
8 20
Find the static and dynamic resistances of the lament and also the power consumption at the operating points (a) i 10 mA; (b) i 15 mA. R V ; I r V ; I p VI
a b
R% R%
2:5 3 2 250 ; r % 500 ; p % 2:5 10 10 3 W 25 mW 10 10 3 11 9 10 3 5 5:5 4:5 333 ; r % 500 ; p % 5 15 10 3 W 75 mW 15 10 3 16 14 10 3
Solved Problems
2.1 A 25.0- resistance has a voltage v 150:0 sin 377t (V). Find the corresponding current i and power p.
i v 6:0 sin 377t A R p vi 900:0 sin2 377t W
The current in a 5- resistor increases linearly from zero to 10 A in 2 ms. At t 2 ms the current is again zero, and it increases linearly to 10 A at t 4 ms. This pattern repeats each 2 ms. Sketch the corresponding v.
Since v Ri, the maximum voltage must be 5 10 50 V. In Fig. 2-10 the plots of i and v are shown. The identical nature of the functions is evident.
An inductance of 2.0 mH has a current i 5:0 1 e 5000t (A). Find the corresponding voltage and the maximum stored energy.
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