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The CPU is the brain of the computer. Its job is to receive data input from the I/O devices (keyboard, mouse, modem, and so on), manipulate the data in some way based on a set of commands from a resident application, and package the newly gerrymandered data for presentation to a human user at another I/O device (monitor). The CPU has its own set of sub-components. These include a clock, an arithmetic-logic unit (ALU), and registers. The clock is the device that provides synchronization and timing to all devices in the computer, and it is characterized by the number of clock cycles per second it is capable of generating. These cycles are called Hertz. Modern systems today operate at 850 to 1,000 Megahertz, or MHz. The faster the clock, the faster the machine can perform computing operations. The ALU is the specialized silicon intelligence in the CPU that performs the mathematical permutations that make the CPU useful. All

Problem 5-2

This is true in any series dc circuit, no matter what the components actually are, and regardless of whether or not they all have the same resistance. If the bulbs in Fig. 5-1 had different resistances, some of them would consume more power than others. In case one of the bulbs in Fig. 5-1 burns out, and its socket is then shorted out instead of filled with a replacement bulb, the current through the whole chain will increase, because the overall resistance of the string will go down. This will force each of the remaining bulbs to carry more current, and pretty soon another bulb would burn out because of the excessive current. If it, too, were replaced with a short circuit, the current would be increased still further. A third bulb would blow out almost right away thereafter.

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In the circuit of Fig. 5-2, what will happen to the voltages across the resistors if one of the 20- resistors is shorted out In this case the total resistance becomes R (10 5) (20 4) 50 80 130 . The current is therefore I E/R 15/130 0.12 A. This is the current at any point in the circuit. This is rounded off to two significant figures. The voltage En across Rn 10 is equal to En I(Rn) 0.12 10 1.2 V.

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The bulbs in the string of Fig 5-1, being all the same, each get the same amount of voltage from the source If there are a dozen bulbs in a 120-V circuit, each bulb has a potential difference of 10 V across it This will remain true even if the bulbs are replaced with brighter or dimmer ones, as long as all the bulbs in the string are identical Look at the schematic diagram of Fig 5-2 Each resistor carries the same current Each resistance Rn has a potential difference En across it equal to the product of the current and the resistance of that particular resistor The voltages En are in series, like cells in a battery, so they add together.

Voltage across parallel resistances 85 The voltage En across Rn 20 is En I(Rn) 0.12 20 2.4 V. Checking the total voltage, we add (5 1.2) (4 2.4) 6.0 9.6 15.6 V. This rounds off to 16 V. Where did the extra volt come from The above is an example of what can happen when you round off to significant figures and then go through a problem a different way. The rechecking process is not part of the original problem. The answers you got the first time are perfectly alright. The figure 16 V is the result of a kind of mathematical trick, a gremlin. If this phenomenon bothers you, go ahead and keep all the digits your calculator will hold, while you do Problem 5-2 and recheck. The current in the circuit, as obtained by means of a calculator, is 0.115384615 A. When you find the voltages to all these extra digits and recheck, the error will be so tiny that it will cancel itself out, and you ll get a final rounded-off figure of 15 V rather than 16 V. Some engineers wait until they get the final answer in a problem before they round off to the allowed number of significant digits. This is because the mathematical bugaboo just described can result in large errors, especially in iterative processes, involving calculations that are done over and over many times. You ll probably never be faced with situations like this unless you plan to become an electrical engineer.

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