Voltage across parallel resistances

Chapter Voltage across parallel resistances

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

  • The voltage En across Rn 20Ω is En I(Rn)0.12202.4 V.Checking the total voltage, we add (5 1.2)(42.4)6.09.615.6 V. Thisrounds 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 fig-ures and then go through a problem a different way. The rechecking process is not partof the original problem. The answers you got the first time are perfectly alright. The fig-ure 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 calculatorwill hold, while you do Problem 5-2 and recheck. The current in the circuit, as obtainedby means of a calculator, is 0.115384615 A. When you find the voltages to all these ex-tra digits and recheck, the error will be so tiny that it will cancel itself out, and you’ll geta 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 roundoff to the allowed number of significant digits. This is because the mathematical buga-boo just described can result in large errors, especially in iterative processes, involvingcalculations that are done over and over many times.You’ll probably never be faced with situations like this unless you plan to become anelectrical engineer.Voltage across parallel resistancesImagine now a set of ornamental light bulbs connected in parallel (Fig. 5-3). This is themethod used for outdoor holiday lighting, or for bright indoor lighting. It’s much easierto fix a parallel-wired string of holiday lights if one bulb should burn out than it is to fixa series-wired string. And the failure of one bulb does not cause catastrophic systemfailure. In fact, it might be awhile before you notice that the bulb is dark, because all theother ones will stay lit, and their brightness will not change.In a parallel circuit, the voltage across each component is always the same and it isalways equal to the supply or battery voltage. The current drawn by each componentdepends only on the resistance of that particular device. In this sense, the componentsin a parallel-wired circuit work independently, as opposed to the series-wired circuit inwhich they all interact.If any one branch of a parallel circuit is taken away, the conditions in the otherbranches will remain the same. If new branches are added, assuming the power supplycan handle the load, conditions in previously existing branches will not be affected.Voltage across parallel resistances855-3Light bulbs in parallel.