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In this circuit, the current can flow from node 1 to node 2 through two different paths i.e either thorugh R2 or (R1+R4). Since the current selects the easier path I expect the current to flow from R2 only. But I often see the combination of resistors being reduced to single equivalent resistance. Is it because the parallel combination further reduces the resistance or anything else? I am sorry if the question is stupid.

schematic

simulate this circuit – Schematic created using CircuitLab

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  • \$\begingroup\$ Yes, the parallel combination further reduces resistance, current will go trough both paths. \$\endgroup\$ Jan 3, 2019 at 15:20
  • \$\begingroup\$ Is this homework? \$\endgroup\$
    – AnalogKid
    Jan 3, 2019 at 15:39

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I really hate that "currrent will take the path of least resistance" expression, as many newbies will see an "only" in it somewhere, which is definitely not correct.

Current will take all possible paths, in inverse propoortion to their resistances. That is, more current will flow in the path of least resistance, but current will flow in all other possible paths as well.

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  • \$\begingroup\$ Thanks Peter. Thats the very famous misconception actually. \$\endgroup\$
    – G-aura-V
    Jan 4, 2019 at 3:38
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The current will take the path of least resistance, but proportionately to the conductance of the path. If one path has twice the resistance, it will get half the current. It's like when one cashier is faster than another one...one is ringing up more merchandise, but they both have about the same length line.

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    \$\begingroup\$ Your first sentence is contradictory, because the word "least" implies that a single path is taken. Also, your cashier analogy makes no sense to me. \$\endgroup\$ Jan 3, 2019 at 16:53
  • \$\begingroup\$ Okay, think of it more like traffic. Even if there's a clear best route, not everyone will take it...for various reasons some people will take detours, but the better routes are more traveled. \$\endgroup\$ Jan 3, 2019 at 21:28
  • \$\begingroup\$ In the traffic analogy, what characteristic corresponds to voltage? What corresponds to resistance? If you want to make an analogy you have to make it meaningful. \$\endgroup\$ Jan 3, 2019 at 21:39

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