How does the total resistance in a system change when additional resistance is added in series?

Answer 1

Sneighke answered: This discussion adds to the original question There are two types of resistance topologies: 1) Series and 2) parallel. To answer your question, resistance added in series always ADD together increasing the total resistance of the circuit. Conversely, adding parallel resistance reduces the total resistance of the circuit. So, for series circuits, R(total) = R1+R2+...Rx Parallel circuits are the exact mathematical inverse. The easiest way to determine parallel resistance is to add the inverse of resistance which is conductance, conductance being 1/r and is stated in Siemens (hold the jokes!...), then taking the inverse of the total conductance to convert back into Ohms. For example, if you have three resistors R1, R2, and R3, and they are parallel connected, the total resistance of the circuit is the inverse of the sum of conductance which would be written as 1 / (1/r1+1/r2+1/r3). By definition, conductance is the inverse of resistance. An example: Given three resistors of 5, 100, and 500 Ohms, In series, R(total) = 5+100+500 = 605 Ohms. In parallel, the total is always less than the lowest resistor: Converting to conductance (used to be called Mhos which is "Ohm" backwards, but has been replaced with the SI unit of Siemens): 5, 100, and 500 Ohms = 1/5+1/100+1/500 = 0.200+0.010+0.002 = 0.212 Siemens. Converting back into resistance, 1/conductance = 1/0.212 Siemens = 4.717 Ohms which as stated above, is less than the lowest resistance resistor. In fact, sometimes working with conductance is easier in series/parallel circuits and, in particular, calculating which values of resistors are required to yield a desired resistance; usually a non-standard resistance value needed for a specific purpose in a circuit. An example: Say you need a non-standard resistance of 698 Ohms. Since we know that parallel resistors create a value lower than the lowest parallel connected resistor, you would start with the next highest standard value and then add a parallel resistor to get you what you need. In this case, you would subtract the desired conductance from the starting resistor: 698 Ohms = 1/698 = 0.001427 Siemens or 1.4327 milliSiemens. If we had a standard value resistor of 750 Ohms (remember, you have to start higher): 750 Ohms = 1.3333 mS. To find the required parallel resistor to get us our 698 Ohms, subtracting the conductances 1.4327mS-1.333mS = 99.33uS (micro Siemens) [0.00009933 S]. Converting back into Ohms, 1/99.33uS = 10.07kOhms (10,070 Ohms) which is close to the standard value of 10kOhms. Doublechecking, Add the conductances: 10,000 Ohms = 100uS 750 Ohms = 1.3333mS Adding gives a total conductance of 1.4333mS. Thus the parallel equivalent = 1/Siemens = 1/0.0014333 = 697.7 Ohms which is within 0.04% of the 698 Ohms we need which is well within acceptable error and we have our 698 Ohm resistor by connecting 10,000 Ohms and 750 Ohms in parallel.