qr code vb.net source * Also called a junction or junction point. in .NET

Encoder Code 128 Code Set B in .NET * Also called a junction or junction point.

* Also called a junction or junction point.
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CHAPTER 4 Basic Network Laws and Theorems
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Kirchhoff s Voltage Law
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Note: before commencing this section you might wish to rst review the meanings of the terms active device and passive device from section 2.5. Consider, now, two points x and y. If we say that x is at a HIGHER VOLTAGE than y, we will mean that x is POSITIVE with respect to y. Thus, going from a point y up to a more positive point x constitutes a RISE in voltage, while going from a point x down to a less positive point y constitutes a DROP in voltage. In other words, going from minus to plus is a voltage rise, whereas going from plus to minus is a voltage drop. We ve already learned that the voltage drop across a resistor of R ohms carrying a current of I amperes is RI volts (eq. (13), Chap. 2), and that the polarity of the voltage drop across a resistor is always PLUS TO MINUS in the direction of the current, as in Fig. 46.
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Fig. 46
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Thus, if we go through a resistor in the same direction as the current we go from plus to minus, which is a voltage drop of RI volts. But if we go through a resistor against the current ow we go from minus to plus, which is a voltage rise of RI volts. We likewise experience a voltage rise if we go through a battery from minus to plus, and a voltage drop if we go through a battery from plus to minus. All the foregoing facts can be summarized as follows. Moving through any circuit element, active or passive, from NEGATIVE TO POSITIVE is a VOLTAGE RISE, while moving from POSITIVE TO NEGATIVE is a VOLTAGE DROP. It should be remembered that the voltage across a resistance is always positive to negative in the direction of the current, as illustrated in Fig. 46. Common sense tells us that if we go completely around a closed path in a circuit the sum of the voltage rises must equal the sum of the voltage drops in the path; that is, there can be no voltage left over in a closed path. In network terminology any closed path is called a loop, and using this term the above fact, concerning voltage drops and rises, is summarized in Kirchho s voltage law: If we go in a speci ed direction completely around any loop (closed path) in any circuit, the sum of the voltage drops equals the sum of the voltage rises in the loop. By speci ed direction we mean clockwise (cw) or counterclockwise (ccw). We can choose either direction but, having made a choice, we must keep that direction throughout the working of a given problem. Let us now illustrate, with the aid of Fig. 47, how the foregoing de nitions are actually applied. Note that Fig. 47 consists of two resistances and two batteries, all in series. Let
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CHAPTER 4 Basic Network Laws and Theorems
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Fig. 47
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us assume the current I is owing in the cw sense around the loop, in which case the polarities ( and ) appear across the resistances as shown. Let us now write the equation for Fig. 47 in accordance with Kirchho s voltage law. To do this, we start at any point, such as A, and move completely around the circuit (we will assume in the cw sense here), listing the voltage drops and the voltage rises as we go. (In doing this, remember that we have de ned that going from minus to plus constitutes a RISE in voltage and going from plus to minus constitutes a DROP in voltage.) Thus, if we agree to list all voltage drops on the left-hand sides of our equations and all the voltage rises on the right-hand sides, the Kirchho voltage equation for Fig. 47 is R1 I V2 R2 I V1 Note that V2 appears as a voltage drop, because we go through that battery from plus to minus ( to ). Or, putting all the battery voltages on the right-hand side, the above equation becomes 57 R1 I R2 I V1 V2 hence I V1 V2 R1 R2
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Notice that if V1 is greater than V2 the current I will be positive, which means that the current does ow in the cw sense, as assumed in Fig. 47. Note, however, that if V2 is greater than V1 then I will be negative, which means that the current I actually ows in the ccw sense, opposite to the direction assumed in Fig. 47. This will be true in general in all our work; thus, a negative value of current will mean that the current actually ows in a sense or direction opposite to what we assumed when we drew the current arrows in the circuit diagram. Problem 46 In Fig. 48, the resistance values are in ohms and the battery emf s are in volts. Let the cw sense be the direction of positive current, as shown. Find I.
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