# Infinity divided by 0? Answered

Does infinity divided by zero theoretically equal any number other than 0 or infinity?
I heard something about ohm's law applied to a circuit with an ideal voltage source (which is only theoretically possible) and having the terminals shorted out and at 0 ohms, resulting in the current going up to infinity?

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The practical point of the lim R->0 game is to figure out what kind of over current protection and over-voltage protection the device is required to have based on its carry load.

Don't knock lim.  lim makes magic into science.

In an ideal crunching game, the answer is infinity. (all fanboys clap your little hands)

In practical electronics or electrical engineering terms, the actual short circuit current is mediated by the intrinsic resistance, capacitance, and inductance of the hardware.

However, we buy a relay that says "10 amps, 220 VAC"...but what happens if you're running a nice inductive motor from that?

Let's say the motor is operating at a quiescent current of 9 amps.

Now. turn off the power circuit. fun begins in microseconds.

the inductor, because of Ldit/dit, does not wreally want to go from N amps to 0 instantaneously...In fact, it with get rather peaviish...its temper will rise, and rise and rise, until it towers over you, until it dispels that energy by flowing into some other path or into the switch.

So the device is rated for 220V right? but the kick back voltage generated by the flywheel...oops, I mean, inductor, can reach significantly higher than that number. Which is why there are relays made for motors and one made for "not motors". in a semiconductor, the voltage can get so high that it literally burns a hole thru the semiconductor junction, one itsy bitsy, totally pissed off lighting bolt encase in black plastic

ramble mode off...I forgot what I was saying.

oh...well the use of the "approaches infinity" idea comes in handy, because it reduces the indeterminacy of governing equations when its results are used to strip variables from the calculation. (called reducing the degrees of freedom.very useful in modeling)

You are dealing with two different constructs. One is mathematical, the other is electrical theory.

Division by zero is mathematical. In mathematics division by zero is undefined. From a practical standpoint you can't divide an orange (or or pie, anything else) by zero. You can divide by 2, 1, .5 .000001, but not zero.

The answer to the short-circuit question is electrical theory, and  "theoretically" the current would approach infinity. One form of Ohm's law to calculate current is: I=E/R. I=current, E=voltage, and R= Resistance. From this simple formula as R gets smaller, I (upper case "i" or current) gets larger. As R approaches 0 (zero), I (upper case 'i') approaches infinity. That's the theoretical side. The practical side shows that the amount of current that will be provided by a short-circuit is limited by the circuit breaker, or device that has the lowest power rating. In a power supply typically a fuse will blow before a component in the power supply.

W/ref the circuit, superconductors will build massive currents, but you're limited but the parts of the circuit that aren't superconductors. You can have the super-conductor in a loop and charge by induction (still limited by your non-superconducting charger though) and build mighty electromagnets:
11.7 Tesla!

L

FTFA.
To understand division by zero, we must check it with multiplication: multiply the quotient by the divisor to get the original number. However, no number multiplied by zero will produce a product other than zero. To satisfy division by zero, the quotient must be bigger than all other numbers, i.e., infinity. This connection of division by zero to infinity takes us beyond elementary arithmetic (see below).

As Orksecurity said, it's an undefined quantity, because the limits give inconsistent results depending on the order in which you evaluate them.

In any practical problem, you cannot actually reach either of the two limits:  a short is not zero resistance, just small (typically milliohm or so), and all current sources have a maximum output.

What happens with a dead short, obviously, is that the current output goes to its maximum and the voltage source is quickly drained, or overheats (that pesky Ohm's law, again, P = I2R).