# Parallel circuit and Ohms law

Theoretical questions with ideal components.(R2 is 10 Ohm)

1) parallel circuit. R1 and ammeter,

If I have a parallel circuit of 2 resistances, both zero Ohm, the current would split to 2 and each current would be half. If the resistor R1 would be 1 pico Ohm, and the ammeter zero Ohm, there would be no current through the resistor, and all the current would go through the ammeter?

2) Ohms law.

R2 is 10 Ohm, current is 1A.

voltage between point A and B is 0 volt, resistance between A and B is 0 Ohm,

according to Ohms law, I = V / R = 0 / 0 = 0 A.

Correction, 0/0 is not 0, it is undefined.(edited after posting)

Is it telling me that it sees this as 2 circuits, with a common wire, and the circuit between A and B has no current, but the circuit between (+) and (-) has 1 Amp.

Correction, the current between A and B is undefined. (edited after posting)

Both questions are theoretical with ideal components, and the voltmeter and ammeter are connected this way on purpose. I would like to get some feedback on this topic.

• There is one problem with your maths: $\frac{x}{0}=\infty$. (Actually "undefined", but infinity is the best approximation in this case). Mar 15, 2015 at 15:47
• 1: Yes, everything you said is correct. For #2, keep in mind that I can be anything (V = IR) if V and R are both zero; there are infinitely many solutions. Mar 15, 2015 at 15:50
• @Majenko, not when x is 0 also. Mar 15, 2015 at 15:51
• @ThePhoton Grab your favourite calculate and enter 0/0 and see what it says. Mar 15, 2015 at 16:03
• @sparkyAl, infinity is not a number. Usually it's a limit. "Infinity divided by infinity" depends what the two infinities are the limit of. Mar 15, 2015 at 16:09

If I have a parallel circuit of 2 resistances, both zero Ohm, the current would split to 2 and each current would be half.

"Zero ohms" is an idealization. If you say you have two zero-ohm resistors in parallel, it just means your model is not accurate enough to determine how the current is split.

If the resistor R1 would be 1 pico Ohm, and the ammeter zero Ohm, there would be no current through the resistor, and all the current would go through the ammeter?

If "zero ohms" means much much less than 1 picoohm, then yes, essentially all the current would go through the ammeter.

But real ammeters have burden resistance that's much much more than a picoohm (more like a few milliohms).

2) Ohms law. R2 is 10 Ohm, current is 1A. voltage between point A and B is 0 volt, resistance between A and B is 0 Ohm, according to Ohms law, I = V / R = 0 / 0 = 0 A.

You have a false conclusion. Zero divided by zero is not zero. It is an undetermined value. Could be zero or could be infinite, depending on the situation.

To analyze this circuit, restate Ohm's law as V = I R. You know the current is 1 A due to the other circuit elements. You know the voltmeter doesn't pass current. Therefore there's 1 A passing from B to A, and because it's a perfect wire, the voltage is zero.

• The Photon, In 2 parallel branches with equal resistance, the current splits to 2 halves, also then if they have both 0 Ohm. But If instead of zero ohm, I would use infinitely small, then the split can't be determined. If one branch would have 0 Ohm, and the other infinitely small resistance, the branch with 0 Ohm resistance would conduct all the current and the branch with infinitely small resistance would not have any current. Am I correct on this? Mar 15, 2015 at 17:34
• @sparkyAl, there's no such thing as a perfect "zero ohm resistor" (except maybe a superconductor). So if you say your model contains two parallel zero-ohm resistors, then it means your model is not accurate enough to predict the current split for any real world situation. Mar 15, 2015 at 17:38
• When we model something as a zero-ohm resistor, we really mean "much smaller than any other resistance it's combined with". You can't have R(A) << R(B) and R(B) << R(A) at the same time. Mar 15, 2015 at 17:39