# Maximum resistance allowing for short circuits

Consider a contrived circuit consisting of only cell and pot:
(1) a cell with constant voltage V and constant amperage A,
(2) variable resistor of resistance R initially set to its highest finite resistance and used to close the circuit with the cell.

(Assume that the variable resistor has a range of zero ohms to infinity ohms, and that its highest finite setting is guaranteed to create a closed circuit that is not a short circuit for arbitrarily large V and A, and that some resistance R greater than zero ohms is guaranteed to be a short circuit.)

Given a closed, non-open, non-short circuit comprised only of a variable resistor of resistance R, and a cell with amperage A and voltage V, what is the value of R when the circuit shorts out as we reduce R from infinity to zero?

• It depends very much on the specific circumstances. We could say that there is some low resistance, Rs where R is effectively a short. And there is some high resistance, Ro where R is effectively open. Practically speaking, it will always be the case that Rs and Ro are not equal. Dec 20 '14 at 17:35
• @mkeith I am not talking about Rs vs Ro (short vs open), but rather Rs vs Rc (closed and short vs closed and not short). Eg, How do I find the point at which Rc - Rs = ε? Dec 20 '14 at 17:47
• It varies for every circuit. Sometimes 10 Ohms is short, and sometimes 100 mOhms is too much. For example, if you are switching an audio signal into a high-impedance load, 10 ohms is short. But if you are switching a 1V supply into a 2A load, 100 mOhms is way too much. Dec 20 '14 at 18:07

When short circuit resistance cause the power supply not to deliver enough current we can say it is a short circuit. Else short circuit resistance is a resistance that is connected parallel to the load.

You cannot simply define a resistance for a short circuit. A short circuit is basically an unintended connection between two nodes, and that is it. Yes, typically they are low resistance paths, but they do not have to be. If you accidentally put a resistor across your VDD/GND rail, you are "shorting" your circuit because you are changing the expected node voltages. The thing is, you can short your circuit between any node. A resistive short across a pair of nodes might be more drastic than another pair.

Consider a contrived circuit consisting of only a cell with constant voltage V and constant amperage A

That's not possible. We can have:

(1) A constant voltage source - the current is determined by the attached resistance.

(2) A constant current source - the voltage is determined by the attached resistance.

(3) Something in-between, e.g., a voltage or current source with internal resistance.

Given a closed, non-open, non-short circuit comprised only of a variable resistor of resistance R, and a cell with amperage A and voltage V, what is the value of R when the circuit shorts out as we reduce R from infinity to zero?

I've read through this a number times and it isn't clear to me exactly what you're asking.

What do you mean by "the circuit shorts out"? Do you mean to ask at what resistance the current becomes maximum such that reducing the resistance further does not cause the current to increase?

• The contrived circuit has two items -- cell and pot. What I mean by "shorting out" is the circuit's entering into a destructive state that will almost instantaneously and indeed certainly disable some component, which may result in an open circuit. Examples: securing a wrench across car battery terminals (destroying the battery most likely) or securing a single hair-thin strand of copper between car battery terminals (heating the strand of copper until part melts or breaks apart and opens the circuit). Dec 20 '14 at 23:20
• @ProductionValues, To almost any EE, "shorted out" does not equate to sparks and overload damage etc. Indeed, we often use the notion of short circuit current in elementary circuit analysis. So, is your question is essentially "what is the value of R at which the cell is damaged?" Dec 20 '14 at 23:46

I assumed your question should read like that " How much minimum resistance required to avoid Short circuit"

Simple answer is 3 root of applied voltage, for example if you are designing a electrical circuit using 3 phase 415 volts, it should be minimum 7.46 ohms resistance required to avoid short circuit

• (1) The question is for a cell and a pot so it's not clear why you are discussing three-phase. (2) Where did you get the idea that R < 7.46 ohms is a short-circuit? Are you mixing this up with $V_{ph-ph} = \sqrt 3 V_{ph-n}$? Welcome to EE.SE. Apr 19 '20 at 13:34