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CIRCUIT CONCEPTS
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The diode of Example 2.4 operates within the range 10 < i < 20 mA. Within that range, approximate its terminal characteristic by a straight line i v , by specifying and . Ans. i 630 v 4407 mA, where v is in V
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The diode of Example 2.4 operates within the range of 20 < i < 40 mA. Within that range, approximate its terminal characteristic by a straight line connecting the two operating limits. Ans. i 993:33 v 702:3 mA, where v is in V
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Within the operating range of 20 < i < 40 mA, model the diode of Example 2.4 by a resistor R in series with a voltage source V such that the model matches exactly with the diode performance at 0.72 and 0.75 V. Find R and V. Ans. R 1:007 ; V 707 mV
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Circuit Laws
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3.1 INTRODUCTION An electric circuit or network consists of a number of interconnected single circuit elements of the type described in 2. The circuit will generally contain at least one voltage or current source. The arrangement of elements results in a new set of constraints between the currents and voltages. These new constraints and their corresponding equations, added to the current-voltage relationships of the individual elements, provide the solution of the network. The underlying purpose of de ning the individual elements, connecting them in a network, and solving the equations is to analyze the performance of such electrical devices as motors, generators, transformers, electrical transducers, and a host of electronic devices. The solution generally answers necessary questions about the operation of the device under conditions applied by a source of energy.
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KIRCHHOFF S VOLTAGE LAW
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For any closed path in a network, Kirchho s voltage law (KVL) states that the algebraic sum of the voltages is zero. Some of the voltages will be sosurces, while others will result from current in passive elements creating a voltage, which is sometimes referred to as a voltage drop. The law applies equally well to circuits driven by constant sources, DC, time variable sources, v t and i t , and to circuits driven by sources which will be introduced in 9. The mesh current method of circuit analysis introduced in Section 4.2 is based on Kirchho s voltage law.
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EXAMPLE 3.1. Write the KVL equation for the circuit shown in Fig. 3-1.
Fig. 3-1
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CIRCUIT LAWS
Starting at the lower left corner of the circuit, for the current direction as shown, we have va v1 vb v2 v3 0 va iR1 vb iR2 iR3 0 va vb i R1 R2 R3
KIRCHHOFF S CURRENT LAW
The connection of two or more circuit elements creates a junction called a node. The junction between two elements is called a simple node and no division of current results. The junction of three or more elements is called a principal node, and here current division does take place. Kirchho s current law (KCL) states that the algrebraic sum of the currents at a node is zero. It may be stated alternatively that the sum of the currents entering a node is equal to the sum of the currents leaving that node. The node voltage method of circuit analysis introduced in Section 4.3 is based on equations written at the principal nodes of a network by applying Kirchho s current law. The basis for the law is the conservation of electric charge.
EXAMPLE 3.2. Write the KCL equation for the principal node shown in Fig. 3-2. i1 i2 i3 i4 i5 0 i1 i3 i2 i4 i5
Fig. 3-2
CIRCUIT ELEMENTS IN SERIES
Three passive circuit elements in series connection as shown in Fig. 3-3 have the same current i. The voltages across the elements are v1 , v2 , and v3 . The total voltage v is the sum of the individual voltages; v v1 v2 v3 .
Fig. 3-3
If the elements are resistors,
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