Kirchhoff’s Current Law (KCL)

Chapter 6.4 Kirchhoff’s Current Law (KCL)

Lessons In Electric Circuits Volume I – DC Book
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Lessons In Electric Circuits Volume I – DC Book

  • 6.4. KIRCHHOFF’S CURRENT LAW (KCL)193RtotalRnEtotalEn = In = ItotalRnRtotalVoltage dividerformulaformulaCurrent dividerIt is quite easy to confuse these two equations, getting the resistance ratios backwards. Oneway to help remember the proper form is to keep in mind that both ratios in the voltage andcurrent divider equations must equal less than one. After all these are dividerequations, notmultiplierequations! If the fraction is upside-down, it will provide a ratio greater than one,which is incorrect. Knowing that total resistance in a series (voltage divider) circuit is alwaysgreater than any of the individual resistances, we know that the fraction for that formula mustbe Rn over RTotal. Conversely, knowing that total resistance in a parallel (current divider)circuit is always less then any of the individual resistances, we know that the fraction for thatformula must be RTotal over Rn.Current divider circuits also find application in electric meter circuits, where a fraction ofa measured current is desired to be routed through a sensitive detection device. Using thecurrent divider formula, the proper shunt resistor can be sized to proportion just the rightamount of current for the device in any given instance:sensitive devicefraction of totalcurrentRshuntItotalItotal• REVIEW:• Parallel circuits proportion, or ”divide,” the total circuit current among individual branchcurrents, the proportions being strictly dependent upon resistances: In = ITotal (RTotal /Rn)6.4Kirchhoff’s Current Law (KCL)Let’s take a closer look at that last parallel example circuit: