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Circuits
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in nity A circuit element with resistance approaching zero is called a short circuit Intuitively, one would expect a short circuit to allow for unimpeded ow of current In fact, metallic conductors (eg, short wires of large diameter) approximate the behavior of a short circuit Formally, a short circuit is de ned as a circuit element across which the voltage is zero, regardless of the current owing through it Figure 228 depicts the circuit symbol for an ideal short circuit Physically, any wire or other metallic conductor will exhibit some resistance, though small For practical purposes, however, many elements approximate a short circuit quite accurately under certain conditions For example, a large-diameter copper pipe is effectively a short circuit in the context of a residential electrical power supply, while in a low-power microelectronic circuit (eg, an FM radio) a short length of 24 gauge wire (refer to Table 22 for the resistance of 24 gauge wire) is a more than adequate short circuit
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Table 22 Resistance of copper wire Number of strands Solid 7 Solid 7 Solid 7 Solid 7 Solid 19 Diameter per strand 00201 00080 00254 00100 00320 00126 00403 00159 00508 00113 Resistance per 1,000 ft ( ) 284 284 180 190 113 119 72 75 45 47
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i + v The short circuit: R=0 v = 0 for any i
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Figure 228 The short circuit
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AWG size 24 24 22 22 20 20 18 18 16 16
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A circuit element whose resistance approaches in nity is called an open circuit Intuitively, one would expect no current to ow through an open circuit, since it offers in nite resistance to any current In an open circuit, we would expect to see zero current regardless of the externally applied voltage Figure 229 illustrates this idea In practice, it is not too dif cult to approximate an open circuit: any break in continuity in a conducting path amounts to an open circuit The idealization of the open circuit, as de ned in Figure 229, does not hold, however, for very high voltages The insulating material between two insulated terminals will break down at a suf ciently high voltage If the insulator is air, ionized particles in the neighborhood of the two conducting elements may lead to the phenomenon of arcing; in other words, a pulse of current may be generated that momentarily jumps a gap between conductors (thanks to this principle, we are able to ignite the air-fuel mixture in a spark-ignition internal combustion engine by means of spark plugs) The ideal open and short circuits are useful concepts and nd extensive use in circuit analysis Series Resistors and the Voltage Divider Rule Although electrical circuits can take rather complicated forms, even the most involved circuits can be reduced to combinations of circuit elements in parallel and
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i + v The open circuit: R i = 0 for any v
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Figure 229 The open circuit
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2
Fundamentals of Electric Circuits
R1 + v1 15 V + _ + v 2 R2 i v3 +
in series Thus, it is important that you become acquainted with parallel and series circuits as early as possible, even before formally approaching the topic of network analysis Parallel and series circuits have a direct relationship with Kirchhoff s laws The objective of this section and the next is to illustrate two common circuits based on series and parallel combinations of resistors: the voltage and current dividers These circuits form the basis of all network analysis; it is therefore important to master these topics as early as possible For an example of a series circuit, refer to the circuit of Figure 230, where a battery has been connected to resistors R1 , R2 , and R3 The following de nition applies:
The current i flows through each of the four series elements Thus, by KVL, 15 = v1 + v2 + v3
De nition Two or more circuit elements are said to be in series if the identical current ows through each of the elements
By applying KVL, you can verify that the sum of the voltages across the three resistors equals the voltage externally provided by the battery:
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