Explain please i'm confused :/

What would happen if a wire having no resistance were connected directly across the terminals of an 8V battery? How much current would result, according to ohm's law?

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    \$\begingroup\$ If you really have zero resistance, the current would be infinite (also assuming the battery has no internal resistance). Neither case exists in reality. \$\endgroup\$ – Roger Rowland Mar 27 '16 at 9:59
  • \$\begingroup\$ Does it cause short circuit? \$\endgroup\$ – Ayan Alee Mar 27 '16 at 10:18
  • \$\begingroup\$ Any amount of resistance across a sufficient current and voltage source will cause a short-circuit. Even a low-ohm resistor across the right sort of battery will cause a short. \$\endgroup\$ – user65586 Mar 27 '16 at 13:08

We need to distinguish between a perfect electronic component and a real one. Real components have lots of complicated properties, whereas perfect ones are much simpler approximations that only exist on paper. Perfect components are usually a pretty good starting point for working out what happens in a circuit, and they are easy to work with. But if the behaviour you get from your calculations is bizarre, it's usually a hint that you need to use a more complicated component model in your calculation.

A perfect wire has no resistance, and a perfect battery always produces exactly the same voltage difference across its terminals. If you connect a perfect wire across a perfect battery, then infinite current flows forever. That is obviously not possible with a real battery and wire. So we need to use a better model for one or both components.

Real wires have some resistance, unless they are made of superconductors and kept cold. Superconductors do exist, so lets keep using our perfect wire model for now.

One of the features of a real battery is an internal resistance. The internal resistance looks like a resistor connected in series with the battery. In a real battery, this resistance will limit the current to something which is not infinite. In most real circuits, this resistance will be larger than the resistance of your not-perfect wire.

So how much current will you get? That depends on the voltage of he battery and the internal resistance. If you connect a wire across an AA battery, the voltage is 1.5V and the internal resistance is about 0.2Ohms, so about 7.5 amps will flow. The battery will get quite hot. If you drop a spanner across the terminals of a car battery, the voltage is 12V and the resistance is about 10mOhm, so about a thousand amps will flow. The battery will probably explode and splatter acid everywhere.

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Let's have a look at Ohm's law:

\$ V = IR \implies I = \frac{V}{R} \$

If we use that formula as is, you can quickly see we're not able have a wire with zero resistance (we'd have division by zero). However, we can see what happens when the resistance gets very close to zero.

\$ I = \lim_{R\to0^+} \frac{V}{R} = \infty \$

So, in theory, current becomes very large (and tends to infinity) when the resistance is very low.

In reality however, if you tried to short circuit a battery, the current would likely be bound by the internal resistance of the battery and the resistance of the wire.

Here's a more realistic theoretic model of your short-circuit scenario.


simulate this circuit – Schematic created using CircuitLab

In this case, you can calculate the current to be \$ I = \frac{V}{R} = \frac{8V}{0.1\Omega + 0.005\Omega} = 76.19A \$ which matches our prediction of Very Large Current. You'll probably damage/burn something with that kind of current if the battery can sustain it.

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  • \$\begingroup\$ But if we suppose no resistance then it cause short circuit? \$\endgroup\$ – Ayan Alee Mar 27 '16 at 10:37
  • \$\begingroup\$ Well sure, I suppose that's a fairly common definition of short circuit. Although, in general, short circuit refers to an accidental lower impedance/resistance path being introduced into a circuit. \$\endgroup\$ – tangrs Mar 27 '16 at 10:38
  • \$\begingroup\$ Stack Exchange isn't a place to get free private tuition. If you post constructive, well-researched questions here, many people will be happy to help. Most people here answer questions out of good will so I don't think you'll get many favourable responses if you ask for free tuition. \$\endgroup\$ – tangrs Mar 27 '16 at 10:44
  • \$\begingroup\$ Okay!, by the way thanks for response, have a great day. \$\endgroup\$ – Ayan Alee Mar 27 '16 at 10:45
  • \$\begingroup\$ Its not for free tuition for forever, I'm first year student of ES engineering but basic concept are little confusing to me i just want to clear it . \$\endgroup\$ – Ayan Alee Mar 27 '16 at 11:03

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