1.3.1 Series and Parallel Combinations of Resistors

Chapter 1.3.1 Series and Parallel Combinations of Resistors

Physics Lecture Notes – Phys 395 Electronics Book
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Physics Lecture Notes – Phys 395 Electronics Book

  • CHAPTER 1. DIRECT CURRENT CIRCUITS101.3.1Series and Parallel Combinations of ResistorsCircuit elements are connected in series when a common current passes through each element.The equivalent resistance Req of a combination of resistors Ri connected in series is given bysumming the voltage drops across each resistor.V=iVi = IiRi,(1.7)Req =iRi.(1.8)If RjRk, where Rk are all the other resistors than Req≈ Rj; the largest resistor wins.Circuit elements are connected in parallel when a common voltage is applied across eachelement. The equivalent resistance Req of a combination of resistors Ri connected in parallelis given by summing the current through each resistorI=iIi =iVRi,(1.9)1Req=IV=i1Ri,(1.10)Req =i Riij=i Rj.(1.11)If RjRk, where Rk are all the other resistors than Req≈ Rj; the smallest resistor wins.The following “divider” circuits are useful combinations of resistors. Believe it or not,they are a super useful concept that will often be used in one form or another; learn it.1.3.2Voltage Divider(a)VoutAB+VinR2R1(b)ABI inR1R2 IoutFigure 1.3: Divider circuits: a) voltage divider and b) current divider.Consider the voltage divider shown in figure 1.3a. The voltage across the input source isVin =(R1 +R2)I and the voltage across the output between terminals A and B is Vout = R2I.The output voltage from the voltage divider in thus