According to Wikipedia, " a common type of short circuit occurs when the positive and negative terminals of a battery are connected together with a low-resistance conductor, like a wire. With low resistance in the connection, a high current exists, causing the cell to deliver a large amount of energy in a short time. The question is how much resistance must a wire have for a short-circuit not to occur?
i think that it depends on material and it's application for example,for heating effect we need low resistance but material should be able to sustain this large current,and this also the reason why we use W(toungeston) in bulb
Voltage= IR so a short circuit is when R is low V/R = I so it depends on the voltage and how much you have. In an ideal circuit the battery has no internal resistance and the wire has no resistance. In the real world batteries have resistance and wires have resistance as well. you can measure the resistance of wires with this equation. R= P l/A where P is a constant according to the specific type of material you have l= length and A is the area of the wire (usually A = pi r^2).
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