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lectric Circuits The Staircase Analogy Electric charge dividing into multiple pathways in a parallel circuit is analogous to people walking down stairs which divide up into separate paths. Imagine being at a large shopping mall; you are descending a rather wide stairway when all of a sudden it breaks up into several smaller stairways. Being in a hurry, you scan the different pathways down the stairs to see which path is least crowded. You finally decide that the left stairway is least crowded and make a "dash" towards it. You know that your "flow rate" will be greatest along the stairway with the least resistance. When the "people flow" divides up into multiple pathways, each pathway has the same change in height (or same gravitational potential drop); yet, the pathway which offers the least resistance will have the greatest flow rate. In an analogous manner, as charge flow divides up into multiple pathways in a parallel circuit, each pathway has the same electric potential drop; yet, the pathway with the least resistance will have the greatest rate of charge flow (i.e., current). 6. In the following circuits, fill in the blanks to indicate the current through the different pathways. Calculate the resistance of each resistor. Then rank the resistance of the resistors (labeled A, B, and C) in order from smallest to largest. 12 V 12 V A A AHA A 12 A A 6 A Ranking of Resistance Ranking of Resistance 7. A three-resistor parallel circuit is created. The resistances of the resistors are 3 9, 6 9, and 9 2. Suppose that one observes the current through the 3 2 resistor to be 6 Amperes. The voltage drop across this 3 2 resistor must be V. This provides sufficient evidence to conclude that the voltage drop across the 6 2 resistor is V and the voltage drop across the 9 2 resistor is V. Therefore, the current in the 6 2 resistor is Amperes and the current in the 9 2 resistor is Amperes. When these three branch currents combine, one would observe that the current in the V battery is Amperes. In summary: R1 = 312 R2 = 612 R3 = 912 I1 = 6 Amps 12 = Amps 1 =. Amps AV1 = _ V AV 2=. V AV 3 =_ V Ibattery =_ Amps AV battery = V AV battery / Ibattery = 8. Consider the circuit at the right. a. There is a voltage drop of _ V across each 2- resistor. b. By Ohm's law, the current in each 2-2 resistor is_ amps. c. The current through the battery is _ amps. d. The resistors in parallel offer a combined resistance of to the charge being pumped by the battery. The Physics Classroom, 2020 Page 16