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Resistance is a measure of the opposition that a circuit offers to the flow of electric current. You can compare it to the diameter of a hose. In fact, for metal wire, this is an excellent analogy: smalldiameter wire has high resistance (a lot of opposition to current), and large-diameter wire has low resistance (not much opposition to current). The type of metal makes a difference too. For example, steel wire has higher resistance for a given diameter than copper wire. The standard unit of resistance is the ohm. This is sometimes symbolized by the uppercase Greek letter omega ( ). You ll sometimes hear about kilohms (symbolized k or k ), where 1 k = 1000 , or about megohms (symbolized M or M ), where 1 M = 1000 k = 1,000,000 . Electric wire is sometimes rated for resistivity. The standard unit for this purpose is the ohm per foot (ohm/ft or /ft) or the ohm per meter (ohm/m or /m). You might also come across the unit ohm per kilometer (ohm/km or /km). Table 2-1 shows the resistivity for various common sizes of solid copper wire at room temperature, as a function of the wire size as defined by a scheme known as the American Wire Gauge (AWG).

Frame Relay does not offer a great deal of granularity when it comes to QoS. The only inherent mechanism is the DE bit described earlier as a way to control network congestion. However, the DE bit is binary. It has two possible values, which means that a customer has two choices: the information being sent is either important or it isn t not particularly useful for establishing a variety of QoS levels. Consequently, a number of vendors have implemented proprietary solutions for QoS management. Within their routers (sometimes called Frame Relay Access Devices [FRADs]) they have established queuing mechanisms that enable customers to create multiple priority levels for differing traffic flows. For example, voice and video, which don t tolerate delay well, could be assigned to a higher-priority queue than the one to which asynchronous data traffic would be assigned. This enables Frame Relay to provide highly granular service. The downside is that this approach is proprietary, which means that the same vendor s equipment must be used on both ends of the circuit. Given the strong move toward interoperability, this is not an ideal solution because it locks the customer into a single-vendor situation.

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An RL circuit works at a frequency of 1.0 MHz. It has a resistance of 10 , and an inductance of 90 H. What is the phase angle This is a rather complicated problem, because it requires several steps. But each step is straightforward. You need to do them carefully, one at a time, and then recheck the whole problem once or twice when you re done calculating. 6.28fL First, find the inductive reactance. This is found by the formula XL 6.28 1.0 90 565 . Then find the ratio XL /R 565/10 56.5. The phase angle is arctan 56.5 89 degrees. This indicates that the circuit is almost purely reactive. The resistance contributes little to the behavior of this RL circuit at this frequency.

Table 2-1. Approximate resistivity at room temperature for solid copper wire as a function of the wire size in American Wire Gauge (AWG).

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Problem 13-6

Wire size, AWG # 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Resistivity, ohms/km 0.52 0.83 1.3 2.7 3.3 5.3 8.4 13 21 34 54 86 140 220 350

Quiz 243 This requires that XL be found over again, for the new frequency. Suppose you decide to use megahertz, so it will go nicely in the formula with microhenrys. A frequency of 10 kHz is the same as 0.010 MHz. Calculating, you get XL 6.28fL 6.28 0.010 90 6.28 0.90 5.65 . The ratio XL /R is then 5.65/10 0. 565. The phase angle is arctan 0.565 29 degrees. At this frequency, the resistance and inductance both play significant roles in the RL circuit.

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