barcode reader vb.net codeproject V = v1 + v2 + v3 in Software

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15 V = v1 + v2 + v3
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and since, according to Ohm s law, the separate voltages can be expressed by the relations v1 = iR1 v2 = iR2 v3 = iR3
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we can therefore write 15 V = i(R1 + R2 + R3 ) This simple result illustrates a very important principle: To the battery, the three series resistors appear as a single equivalent resistance of value REQ , where REQ = R1 + R2 + R3 The three resistors could thus be replaced by a single resistor of value REQ without changing the amount of current required of the battery From this result we may extrapolate to the more general relationship de ning the equivalent resistance of N series resistors:
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N series resistors are equivalent to a single resistor equal to the sum of the individual resistances
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REQ =
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which is also illustrated in Figure 230 A concept very closely tied to series resistors is that of the voltage divider This terminology originates from the observation that the source voltage in the circuit of Figure 230 divides among the three resistors according to KVL If we now observe that the series current, i, is given by i= 15 V 15 V = REQ R1 + R 2 + R 3
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we can write each of the voltages across the resistors as: R1 (15 V) v1 = iR1 = REQ v2 = iR2 = v3 = iR3 = That is: R2 (15 V) REQ R3 (15 V) REQ
The voltage across each resistor in a series circuit is directly proportional to the ratio of its resistance to the total series resistance of the circuit
An instructive exercise consists of verifying that KVL is still satis ed, by adding the voltage drops around the circuit and equating their sum to the source voltage: R1 R2 R3 v1 + v 2 + v 3 = (15 V) + (15 V) + (15 V) = 15 V REQ REQ REQ since REQ = R1 + R2 + R3 Therefore, since KVL is satis ed, we are certain that the voltage divider rule is consistent with Kirchhoff s laws By virtue of the voltage divider rule, then, we can always determine the proportion in which voltage drops are distributed around a circuit This result will be useful in reducing complicated circuits to simpler forms The general form of the voltage divider rule for a circuit with N series resistors and a voltage source is: Rn vS R1 + R 2 + + R n + + R N
vn =
Voltage divider
(220)
EXAMPLE 28 Voltage Divider
Problem
Determine the voltage v3 in the circuit of Figure 231
+ v3 +
VS + R1 i R2 v2 R3 v1 +
Solution
Known Quantities: Source voltage, resistance values Find: Unknown voltage v3
VS = 3 V Figure 231
Schematics, Diagrams, Circuits, and Given Data: R1 = 10 ; R2 = 6 ; R3 = 8 ;
2
Fundamentals of Electric Circuits
Analysis: Figure 231 indicates a reference direction for the current (dictated by the
polarity of the voltage source) Following the passive sign convention, we label the polarities of the three resistors, and apply KVL to determine that VS v1 v2 v3 = 0 The voltage divider rule tells us that v3 = VS R3 8 =1V =3 R1 + R2 + R3 10 + 6 + 8
Comments: Application of the voltage divider rule to a series circuit is very
straightforward The dif culty usually arises in determining whether a circuit is in fact a series circuit This point is explored later in this section, and in Example 210
Focus on Computer-Aided Tools: The simple voltagedivider circuit introduced in this
example provides an excellent introduction to the capabilities of the Electronics Workbench, or EWBTM , a computer-aided tool for solving electrical and electronic circuits You will nd the EWBTM version of the circuit of Figure 231 in the electronic les that accompany this book in CD-ROM format This simple example may serve as a workbench to practice your own skills in constructing circuits using Electronics Workbench
Parallel Resistors and the Current Divider Rule A concept analogous to that of the voltage divider may be developed by applying Kirchhoff s current law to a circuit containing only parallel resistances
De nition Two or more circuit elements are said to be in parallel if the identical voltage appears across each of the elements
Figure 232 illustrates the notion of parallel resistors connected to an ideal current source Kirchhoff s current law requires that the sum of the currents into, say, the top node of the circuit be zero: iS = i1 + i2 + i3
KCL applied at this node + i1 iS R1 i2 R2 i3 R3 v The voltage v appears across each parallel element; by KCL, iS = i1 + i2 + i3 R1 R2 R3 Rn RN REQ
N resistors in parallel are equivalent to a single equivalent resistor with resistance equal to the inverse of the sum of the inverse resistances
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