Kirchhoff’s first law

Chapter Kirchhoff’s first law

Teach Yourself Electricity and Electronics Third Edition Book
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Teach Yourself Electricity and Electronics Third Edition Book

  • First find E 2, because you’ll be needing that number often: E 23.03.09.0.Then P19.0/220.4091 W, P29.0/470.1915 W, P39.0/680.1324 W. Thesecan be rounded off to P10.41 W, P20.19 W, and P30.13 W. But remember thevalues to four places for the next problem.In a parallel circuit, the total power consumed is equal to the sum of the wattagesdissipated by the individual resistances. In this respect, the parallel circuit acts like theseries circuit. Power cannot come from nowhere, nor can it vanish. It must all be ac-counted for.Problem 5-10Find the total consumed power of the resistor circuit in Problem 5-9 using two differentmethods.The first method involves adding P1, P2, and P3. Let’s use the four-significant-digitvalues for “error reduction insurance.” The sum is P0.40910.19150.132407330 W. This can be rounded to 0.73 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 R12.28Ω. Then PE 2/R 9.0/12.280.7329 W. This can be rounded to0. 73 W or 730 mW.In pure mathematics and logic, the results are all deduced from a few simple, intu-itively appealing principles called axioms. You might already know some of these, suchas Euclid’s geometry postulates. In electricity and electronics, complex circuit analysiscan be made easier if you are acquainted with certain axioms, or laws. You’ve alreadyseen 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 thevoltage across any other, or across the whole set.• The voltages across elements in a series circuit always add up to the supplyvoltage.• The currents through elements in a parallel circuit always add up to the totalcurrent drawn from the supply.• The total power consumed in a series or parallel circuit is always equal to thesum of the wattages dissipated in each of the elements.Now you will learn two of the most famous laws in electricity and electronics. Thesemake it possible to analyze extremely complicated series-parallel networks. That’s notwhat you’ll be doing in this course, but given the previous axioms and Kirchhoff’s Lawsthat follow, you could if you had to.Kirchhoff’s first lawThe physicist Gustav Robert Kirchhoff (1824-1887) was a researcher and experimen-talist in electricity back in the time before radio, before electric lighting, and beforemuch was understood about how currents flow.Kirchhoff’s first law89