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It is proven only when there is a potential difference current flows in that branch between two nodes, then how we say that the current flows in a short circuit where the voltage on that branch is 0?

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  • \$\begingroup\$ Ohm's Law, three forms: (i) \$V=IR =0\$; (ii) \$R=\frac{V}{I}=0\$; (iii) \$I=\frac{V}{R}=\frac{0}{0} = \text {indeterminate}\$ \$\endgroup\$ – Chu Jun 20 at 8:21
  • \$\begingroup\$ This is one of the most frequently asked questions on the site. Unfortunately it's not the easiest to search for, but please do make an attempt. The Q&A I linked above is probably not the clearest example, just the first I could find. \$\endgroup\$ – The Photon Jun 20 at 14:34
  • \$\begingroup\$ Here's another example: Why is it that current pass from charger to battery while both of them have the same voltage? \$\endgroup\$ – The Photon Jun 20 at 14:36
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    \$\begingroup\$ The answer to your hypothetical question is like asking what is 0/0. \$\endgroup\$ – Mitu Raj Jun 20 at 18:39
  • \$\begingroup\$ In the idealized model of basic circuit analysis, wires are not physical wires, but a way of saying which is connected to which. When you connect two points together, they have the same voltage, and in fact, they're literally considered as the same point, or node. A short circuit is like saying "let +5 V and 0 V be the same thing", which is self-contradictory. Thus, a short circuit is meaningless and illegal in circuit theory, like division by zero. At best, you can think of "what would happen as a resistor between them approaches zero", but not a direct connection without anything in between. \$\endgroup\$ – 比尔盖子 Jun 20 at 20:56
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It is proven only when there is a potential difference current flows in that branch between two nodes ...

No, it's not.

If there's a resistor between those two nodes, then yes.

If there's zero resistance, then whatever current that there is flowing will generate no voltage. Just think of a superconductor.

If there's an inductor between the two nodes, then you can have a current flowing, with the voltage related to how fast the current is changing, not to the actual value of the current.

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Superconductors aside...

In a real and practical circuit, there is no such thing as 'zero resistance', ergo no such thing as 'infinite current', which is what one might expect from the math.

Besides unavoidable wire resistance, there is also a 'source impedance'... Real voltage sources always have some internal resistance. In an actual short circuit, the source impedance would be what limits the current to something less than infinity.

As a simple example - In an alkaline battery, there's about 1/4 to 1 ohm resistance, meaning from a typical AA, C, D etc you're limited to a few amps even if you short the terminals with a superconducting wire. After some time, the battery starts to get hot. That's caused by the power being dissipated over the internal resistance.

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  • \$\begingroup\$ No prob. Great question actually. $$$$ In engineering -- Heck in many branches of science even -- the models are just simple approximations. "First order effects" we might call them. If one attempts to take into account all the secondary effects, the models become unnecessarily complex. For example - If you are calculating the free fall time of a metal ball being dropped from a tower, you generally would neglect air resistance. It's there, but the effect isn't enough to change your answer enough to make it worth considering. \$\endgroup\$ – Kyle B Jun 20 at 6:31
  • \$\begingroup\$ @HenryBarath.M.A When you write a comment you are explicitly told not to write simple "thank you" notes. \$\endgroup\$ – pipe Jun 20 at 15:29
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... how we say that the current flows in a short circuit where the voltage on that branch is 0?

schematic

simulate this circuit – Schematic created using CircuitLab

Figure 1. There is a short-circuit between A and B.

I can think of two ways of looking at the problem.

  1. A and B are the same node of the circuit. Current through that node is determined by the other elements of the circuit.
  2. If current didn't flow from A to B then VA-B would rise to a non-zero value and the current would have to flow.
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