vb.net barcode reader source code Another Use of the Passive Sign Convention in Software

Printer Denso QR Bar Code in Software Another Use of the Passive Sign Convention

EXAMPLE 25 Another Use of the Passive Sign Convention
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Problem
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Determine whether a given element is dissipating or generating power from known voltages and currents
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Solution
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Known Quantities: Voltages across each circuit element; current in circuit Find: Which element dissipates power and which generates it
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420 A + Element 1000 V A (a) 420 A + 1000 V (b) B Element B
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Schematics, Diagrams, Circuits, and Given Data: Voltage across element A: 1,000 V
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Current owing into element A: 420 A See Figure 216(a) for voltage polarity and current direction
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Analysis: According to the passive sign convention, an element dissipates power when
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current ows from a point of higher potential to one of lower potential; thus, element A acts as a load Since power must be conserved, element B must be a source [Figure 216(b)] Element A dissipates (1,000 V) (420 A) = 420 kW Element B generates the same amount of power
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Comments: The procedure described in this example can be easily conducted
experimentally, by performing simple current and voltage measurements Measuring devices are discussed in Section 28
Check Your Understanding
21 Compute the current owing through each of the headlights of Example 22 if each headlight has a power rating of 50 W How much power is the battery providing
Part I
Circuits
22 Determine which circuit element in the illustration (below, left) is supplying power and which is dissipating power Also determine the amount of power dissipated and supplied
+ 22 A A + 14 V 4V B
23 If the battery in the accompanying diagram (above, right) supplies a total of 10 mW to the three elements shown and i1 = 2 mA and i2 = 15 mA, what is the current i3 If i1 = 1 mA and i3 = 15 mA, what is i2
CIRCUIT ELEMENTS AND THEIR i-v CHARACTERISTICS
The relationship between current and voltage at the terminals of a circuit element de nes the behavior of that element within the circuit In this section we shall introduce a graphical means of representing the terminal characteristics of circuit elements Figure 217 depicts the representation that will be employed throughout the chapter to denote a generalized circuit element: the variable i represents the current owing through the element, while v is the potential difference, or voltage, across the element Suppose now that a known voltage were imposed across a circuit element The current that would ow as a consequence of this voltage, and the voltage itself, form a unique pair of values If the voltage applied to the element were varied and the resulting current measured, it would be possible to construct a functional relationship between voltage and current known as the i-v characteristic (or voltampere characteristic) Such a relationship de nes the circuit element, in the sense that if we impose any prescribed voltage (or current), the resulting current (or voltage) is directly obtainable from the i-v characteristic A direct consequence is that the power dissipated (or generated) by the element may also be determined from the i-v curve Figure 218 depicts an experiment for empirically determining the i-v characteristic of a tungsten lament light bulb A variable voltage source is used to apply various voltages, and the current owing through the element is measured for each applied voltage We could certainly express the i-v characteristic of a circuit element in functional form: i = f (v) v = g(i) (211)
+ v
Figure 217 Generalized representation of circuit elements
In some circumstances, however, the graphical representation is more desirable, especially if there is no simple functional form relating voltage to current The simplest form of the i-v characteristic for a circuit element is a straight line, that is, i = kv (212)
2
Fundamentals of Electric Circuits
i (amps) 05 04 03 02 01 60 50 40 30 20 10 0 01 10 20 30 40 50 60 v (volts)
Current meter i Variable voltage source + v
02 03 04 05
Figure 218 Volt-ampere characteristic of a tungsten light bulb
i 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 v i-v characteristic of a 3-A current source
i 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 v i-v characteristic of a 6-V voltage source
Figure 219 i-v characteristics of ideal sources
with k a constant In the next section we shall see how this simple model of a circuit element is quite useful in practice and can be used to de ne the most common circuit elements: ideal voltage and current sources and the resistor We can also relate the graphical i-v representation of circuit elements to the power dissipated or generated by a circuit element For example, the graphical representation of the light bulb i-v characteristic of Figure 218 illustrates that when a positive current ows through the bulb, the voltage is positive, and that, conversely, a negative current ow corresponds to a negative voltage In both cases the power dissipated by the device is a positive quantity, as it should be, on the basis of the discussion of the preceding section, since the light bulb is a passive device Note that the i-v characteristic appears in only two of the four possible quadrants in the iv plane In the other two quadrants, the product of voltage and current (ie, power) is negative, and an i-v curve with a portion in either of these quadrants would therefore correspond to power generated This is not possible for a passive load such as a light bulb; however, there are electronic devices that can operate, for example, in three of the four quadrants of the i-v characteristic and can therefore act as sources of energy for speci c combinations of voltages and currents An example of this dual behavior is introduced in 8, where it is shown that the photodiode can act either in a passive mode (as a light sensor) or in an active mode (as a solar cell) The i-v characteristics of ideal current and voltage sources can also be useful in visually representing their behavior An ideal voltage source generates a prescribed voltage independent of the current drawn from the load; thus, its i-v characteristic is a straight vertical line with a voltage axis intercept corresponding to the source voltage Similarly, the i-v characteristic of an ideal current source is a horizontal line with a current axis intercept corresponding to the source current Figure 219 depicts these behaviors
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