How come the current is not determined only by the first resistor it encounters?

Question

I was reading about circuits on this link, where they use a tollbooth analogy to explain electricity. Now either this is a bad analogy or I am missing something, but let's consider a circuit that consist of one resistor in series, followed by 2 resistors in parallel. By adding resistor to the parallel part of the circuit, the overall current increases. Let's say the first resistor is a tollbooth, that passes through 1 car per second. Isn't that what determines the current in the whole circuit? The current is 1. Why does adding more tollbooths in parallel speed up the cars? I understand they could go faster, once they pass the first resistor. But why are they able to pass it faster?

To ask it another way, if you are able to eat 2 cookies per second, but I am only giving you one cookie, you can't eat 2 of them each second. Now it doesn't matter if suddenly you can eat 3 cookies per second, if I am able only to give you one.

Answer 1

You are only considering a perfect current source. If the battery has internal resistance, you would not be able to have a higher current when putting resistors in parallel.

Now instead of looking it as a toll booth, look at resistors like a toll that lets only some percentage of cars through, while vaporising the rest. If you connect those tolls in series, each toll limits further the amounts of cars. If you connect them in parallel, they will let more cars through.

Eg. First booth lets 5 cars pass after reaching a queue of 10 cars. Second booth lets 1 car pass after reaching a queue of 10 cars.

The total throughput would be 1 car per 20 cars.

Now if you add a booth in parallel of the second booth, and it also lets 1 car pass after reaching a queue of 10 cars, and since the queues are shared between both booths, you will get 2 cars per 20 cars as throughput.

So step by step:

• 10 cars come to the first booth.
  5 cars go through, they queue behind the two parallel booths. the 5 other are vaporised
• 10 other cars come to the first booth.
  again, 5 cars go through.
• Now each parallel booth lets one cars go through, and vaporises the 8 others.
  2 cars come out.

You have a throughput of 2 cars per 20 car.