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If voltage is equal across parallel resistors, then why can't one battery supply power to a infinite number of leds, if they are all in parallel?

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up vote 13 down vote accepted

Because a battery, like any real power source, has an output impedance. The more current you draw, the lower the voltage output. Granted, for a battery the output is not simply a fixed resistor, but the principle remains the same.

As an example, let's pretend that a 12-volt battery has a 0.1 ohm output impedance. If you were to short the outputs of this notional battery, the current would be 12 v / 0.1 ohms, or 120 amps. By the same token, if a load were to draw 60 amps, the output of the battery would be 12 - (60 * 0.1), or 6 volts.

Another way to put it is that the output impedance sets an upper limit on the amount of power a battery (or any power source) can provide. For DC, this upper limit is (V * V / R) /4. In the case of our notional battery, this upper limit is 360 watts.

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Because it doesn't store an infinite amount of energy, nor can it move the energy it does store at an infinite rate. A chemical process is happening when the battery provides current and it can't happen faster or for longer than the chemicals can proceed.

Even a huge voltage supply powered directly from the electrical grid couldn't power an "infinite" number of LEDs. Infinity is a number beyond the capacity of electrical engineers to design around. In a simulator where you can define a voltage source to have infinite capacity to deliver current it might work fine, but never in the real world.

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"In a simulator where you can define a voltage source to have infinite capacity to deliver current it might work fine, but never in the real world" Why would one oven dare to use the term "infinity' carelessly in the engineering context. Simulation can get you the best fires burning inside the ocean but only in the screen of the simulation and not in the Atlantic. Simply Overall Output can never be greater than Overall input and we all know that from the high school. – javaprince EMBEDDED May 28 '14 at 21:34
Why bother to use the term "infinity" in any context? We can't see past the edge of the observable universe, so we'll never have access to an infinite amount of anything. It's a mathematical construct. In engineering it's more of a placeholder for "a number so big that we don't have to care about how big it is." Maybe OP is a teenage hobbyist building LED blinkies and didn't take high school calculus yet. – Matt B. May 29 '14 at 20:22

A single LED requires a finite amount current. To have infinite LEDs means you need infinite current. This is not possible. Aside from the fact that batteries can not provide infinite current (they have internal impedance), to supply infinite current requires infinite power, to supply infinite power for any duration at all requires infinite energy. Incidentally, batteries do not contain infinite energy.

You can not hook up an infinite number of LEDs because you can not do impossible things. Sorry about that.

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In this case more LEDs in parallel, with the same battery, will imply less current available to each branch of the circuit. Bellow a certain point the LEDs will stop producing light and the current will tend to zero:

  • 3 LED -> I/3 A
  • 5 LED -> I/5 A
  • INF LED -> I/INF -> ~0 A
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