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The sum of all the voltages, as you go around a circuit from some fixed point and return there from the opposite direction, and taking polarity into account, is always zero. Does this seem counterintuitive Let s think about it a little more carefully. What Kirchhoff was expressing, when he wrote his second law, is the principle that voltage cannot appear out of nowhere, nor can it vanish. All the potential differences must ultimately cancel each other out in any closed dc circuit, no matter how complicated that circuit happens to be. This is Kirchhoff s Second Law. We can also call it Kirchhoff s Voltage Law or the principle of conservation of voltage. Remember the rule you ve already learned about series dc circuits: The sum of the voltages across all the individual resistances adds up to the supply voltage. This statement is true as far as it goes, but it is an oversimplification, because it ignores polarity. The polarity of the potential difference across each resistance is opposite to the polarity of the potential difference across the battery. So when you add up the potential differences all the way around the circuit, taking polarity into account for every single component, you always get a net voltage of zero. An example of Kirchhoff s Second Law is shown in Fig. 5-6. The voltage of the battery, E, has polarity opposite to the sum of the potential differences across the resistors, E1 + E2 + E3 + E4. Therefore, E + E1 + E2 + E3 + E4 = 0. 5-6 Kirchhoff s Second Law. The

Premises technologies, including LANs, wireless solutions, and the content that rides on both of them, are the most visible components of the overall network to a customer. In the next chapter, we dive into the network itself and explore the access technologies that provide the bridge between premises technologies and the transport network.

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Find the total consumed power of the resistor circuit in Problem 5-9 using two different methods The first method involves adding P1, P2, and P3 Let s use the four-significant-digit values for error reduction insurance The sum is P 04091 01915 013240 7330 W This can be rounded to 073 W or 730 mW The second method involves finding the resistance R of the parallel combination You can do this calculation yourself, keeping track for four digits for insurance reasons, getting R 1228 Then P E 2/R 90/1228 07329 W This can be rounded to 0 73 W or 730 mW In pure mathematics and logic, the results are all deduced from a few simple, intuitively appealing principles called axioms You might already know some of these, such as Euclid s geometry postulates.

sum of the voltages across the resistances is equal to, but has opposite polarity from, the supply voltage. Therefore, E + E1 + E2 + E3 + E4 = 0. Illustration for Quiz Questions 15 and 16.

In electricity and electronics, complex circuit analysis can be made easier if you are acquainted with certain axioms, or laws You ve already seen some of these in this chapter They are: The current in a series circuit is the same at every point along the way The voltage across any component in a parallel circuit is the same as the voltage across any other, or across the whole set The voltages across elements in a series circuit always add up to the supply voltage The currents through elements in a parallel circuit always add up to the total current drawn from the supply The total power consumed in a series or parallel circuit is always equal to the sum of the wattages dissipated in each of the elements Now you will learn two of the most famous laws in electricity and electronics.

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These make it possible to analyze extremely complicated series-parallel networks That s not what you ll be doing in this course, but given the previous axioms and Kirchhoff s Laws that follow, you could if you had to..

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