During a short-circuit, 'theoretically' current becomes infinite. But what about the emf?

My attempt: Since the potential difference is zero, I guess the emf should also be zero. But again since p.d. is zero, how can current become infinite? At this point, I am considering James Large answer.

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    $\begingroup$ It is not possible to answer the question, as there is insufficient context. A 'short circuit' is just an electrical connection, just like any other (albeit an unintended one). The EMF across a short will depend on the materials/components/voltage sources in the rest of the circuit. $\endgroup$ – Time4Tea Aug 20 '18 at 15:05
  • $\begingroup$ > "During a short-circuit, 'theoretically' current becomes infinite." This is not generally true. Only in some cases, where voltage is maintained by a hard supplier and only somewhat changed by the shorting wire, is the current high. In other cases shorting two points in a circuit just fixes their potential to same value without any extreme current event occuring. $\endgroup$ – Ján Lalinský Jan 2 '19 at 21:20
  • $\begingroup$ An analogy might help. Consider the opposite of what you seek: the value of EMF when you open a switch. Theory may say that the EMF changes instantly -- practice shows a different answer $\endgroup$ – Cort Ammon May 6 '19 at 15:28
  • $\begingroup$ The reading you get on a voltmeter will depend on the internal resistance of the power supply, the resistance of the rest of the circuit, and where you connect the meter. $\endgroup$ – R.W. Bird Jan 8 at 15:44

Your question is incomplete, but it sounds like you might be asking what would happen if you short circuit an ideal voltage source.

The answer is, you can't ask that question. An ideal voltage source is not a real thing. It is a useful part of a theory that we use to describe electronic circuits. But the circuit I just described, a shorted ideal voltage source, is a circuit that can not physically exist.

Real electric power supplies often are designed to approximate an ideal voltage source. But a more accurate model of a real power supply would be constructed from an ideal voltage source plus other ideal components that would limit the current in the case of a short circuit. In the more accurate model, both voltage and current would be well defined, finite numbers everywhere.

Another way of looking at it: The voltage across the terminals of an ideal voltage source, by definition, is not zero. The voltage across the terminals of a zero-ohm resistor, by Ohm's law, must be zero. If you connect them in parallel, the voltage across both components, by Kirchoff's laws, must be the same.

What does it mean when a theory says that it is impossible for two values to be different, and the same theory says that it is impossible for them to be the same? It means that you have asked a question that the theory can not answer.

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What is emf?

"Electromotive force, abbreviated emf (denoted $\varepsilon $ and measured in volts), is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator." (Wikipedia)

What is potential difference?

Voltage, electric potential difference, electric pressure or electric tension...is the difference in electric potential between two points. (Ref)

So emf is the 'pressure' that drives current (caused by e.g. a battery), and potential difference is a measure of the difference in this 'pressure' between any two points in a circuit.

  • During a short circuit, this 'pressure' causing current, emf, continues and drives the current.
  • During a short circuit, there is no resistance in the external circuit between the $+$ and $-$ terminals of the emf driver (e.g. battery), therefore potential difference is zero.
  • However, inside an emf-causing component such as a battery, sub cells will have potential difference (and indeed emf) greater than zero across them, causing the overall emf.
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